UC-NRLF 


DEPARTMENT   OF   COMMERCE 

U.  S.  COAST  AND  GEODETIC  SURVEY 


O.    H. 

SUPERINTENDENT 


SURVEYING 


A   PLANE  TABLE  MANUAL 


BY 


D.    B. 


Assistant 


APPENDIX   No.   7-REPORT   FOR   1905 

( Reprint  with  corrections,  January,  1915 ) 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1915 


GIFT   Of 


DEPARTMENT  OF  COMMERCE 

U.  S.  COAST  AND  GEODETIC  SURVEY 


O.    H. 

SUPERINTENDENT 


SURVEYING 


A  PLANE  TABLE  MANUAL 


BY 


D.    IB. 


Assistant 


APPENDIX  NO.  7— REPORT  FOR  1905 
(Reprint  with  corrections,  January,  1915) 


WASHINGTON 

GOVERNMENT   PRINTING  OFFICE 
1915 


1  /\  o 


ADDITIONAL  COPIES 

OF  THIS  PUBLICATION  MAY  BE  PROCURED  FROM 

THE  SUPERINTENDENT  OF  DOCUMENTS 

GOVERNMENT  PRINTING  OFFICE 

WASHINGTON,  D.  C. 

AT 

50  CENTS  PER  COPY 


CONTENTS. 


PRELIMINARY  STATEMENT. 

Definitions:  Page. 

Topographic  map 295 

Projection. , 295 

Scale 295 

Datum  plane 295 

Relief 295 

Control 295 

INSTRUMENTS. 

Plane  table 296 

Description 296 

The  board 296 

Movements 296 

Tripod 297 

Mountain  plane  table 297 

The  alidade 297 

Description " 297 

Declinatoire 298 

Metal  clamps 298 

Adjustments 298 

Fiducial  edge  of  rule 298 

Levels  attached  to  rule 298 

Parallax 299 

Axis  of  revolution 299 

Vertical  line  of  diaphragm 299 

Middle  horizontal  line  of  diaphragm 299 

Stadia  rod 300 

Description 300 

Graduation 300 

Inclined  sights 301 

Micrometer  eyepiece .' 301 

Plane-table  sheet 302 

Scale  302 

Projections 303 

Selecting  limits 303 

Polyconic  projection 304 

Method  of  constructing 304 

Rectangular 305 

Accessories 305 

Weights 306 

291 


392  CONTENTS. 

FIELD  WORK. 

Page. 

Organization  of  party 306 

Preliminary  reconnaissance 307 

Signal  poles 307 

Graphic  triangulation 307 

Amount  of  control 309 

Three-point  problem 310 

Lehman's  method 311 

Rule  i 311 

Rules  2  and  3 311 

Procedure 311 

Examples 312 

Repetition 312 

Orienting  by  estimation 313 

Bessel's  method  by  inscribed  quadrilateral 313 

Tracing  cloth  protractor 314 

Two-point  problem 314 

Deflection  of  long  lines 315 

Distortion  errors 316 

Position  by  compromise 317 

Application 317 

Height  of  instrument 318 

Relief 318 

Hill  shading 318 

Contours 318 

Profile 319 

Advantages  and  disadvantages  of  contours  and  hill  shading 319 

Contour  interval 319 

Datum  plane 320 

Reference  signal 320 

Station  routine 321 

Number  of  elevations  to  be  determined 321 

Contour  sketching • 321 

Typical  contour  groups , „ 321 

Order  of  development  of  contours 322 

Filling  in 322 

Traverse  lines 322 

Determinations  for  hydrography 323 

High- water  and  storm-water  line 324 

Determination  of  inaccessible  points 324 

Large  scale  surveys 324 

Rapid  surveys 325 

Military  reconnaissance  with  plane  table 325 

With  compass  and  notebook 326 

Photogrammetry 326 

Survey  in  advance  of  triangulation 327 

Office  work 328 

Tables  and  formulae 330 


ILLUSTRATIONS. 


Page. 

1.  Plane  table  and  alidade 296 

2.  Plane  table  movement 296 

3.  Alidade 297 

4.  Stadia  rods 300 

5.  Diagram,  Construction  of  projection 30^ 

6.  Graphic  triangulation 307 

7.  Three-point  problem 3 10 

8.  Three-point  and  two-point  problems 312 

9.  Bessels's  solution  of  three-point  problem 313 

10.  Diagram  illustrating  effect  of  distortion  of  plane  table  sheets 316 

11.  Hypsograph 318 

12.  Hypsograph,  section  and  views 318 

13.  Diagram,  Construction  of  profile  from  plan 319 

14.  Crest,  face,  and  talus  of  a  granite  cliff 319 

15.  Elevation  of  a  granite  cliff 319 

16.  Typical  contour  groups 321 

17.  Conventional  signs 342 

18.  Conventional  signs 342 

19.  Conventional  signs 342 

20.  Conventional  signs 342 

21.  Conventional  signs ' 342 

22.  Conventional  signs • 342 

23.  Conventional  signs 342 

24.  Conventional  signs 342 

25.  Conventional  signs 342 

26.  Conventional  signs 342 

27.  Conventional  signs , 342 

28.  Conventional  signs 342 

29.  Specimens  of  lettering 342 

30.  Sparsely  settled  town,  salt  marsh,  pine  woods,  etc 342 

31.  Railroads,  canals,  iron  bridges,  etc 342 

32.  Eroded  drift  banks,  with  bowlders  set  free 342 

33 .  Blocking  of  cities,  etc 342 

34.  Erosion  of  soft  stratified  rock 342 

35.  Scale  of  hill  curves 342 

36.  Scale  of  shade 342 

37.  Diagram  for  reading  elevations 342 

293 


APPENDIX    7. 


A    PLANK    TABLE    MANUAL. 


By  D.  B.  WAINWRIGHT,  Assistant. 


PRELIMINARY  STATEMENT.* 

A  topographic  map  is  the  delineation  upon  a  plane  surface,  by  means  of  conven- 
tional signs,  of  the  natural  and  artificial  features  of  a  locality. 

Every  point  of  the  drawing  corresponds  to  some  geographic  position,  according 
to  some  method  adopted  for  representing  the  surface  of  the  spheroid  on  a  plane,  which 
is  called  the  projection. 

Since  it  is  a  representation  in  miniature,  the  distance  between  any  two  points  on 
the  map  is  a  certain  definite  fraction  of  the  distance  between  the  same  points  in  nature. 
This  ratio  is  called  the  scale. 

Each  point,  besides  being  projected  on  a  horizontal  plane,  has  its  elevation  rela- 
tive to  a  level  surface,  in  some  way  indicated.  The  level  surface  adopted  for  the  map 
is  called  the  datum  plane,  and  the  representation  of  the  variations  in  the  vertical  ele- 
ment, the  modeling  of  the  country,  is  called  the  relief. 

CONTROL. 

All  topographic  surveys  of  importance  are  based  upon  a  system  of  triangulation. 

A  sufficient  number  of  points,  whose  geographical  positions  have  been  determined 
by  triangulation,  properly  distributed  over  the  area  to  be  surveyed,  forms  the  frame- 
work for  controlling  the  accurate  location  of  the  various  details. 

*  Advantage  has  been  taken  of  the  opportunity  afforded  by  the  preparation  of  a  new  edition  of 
the  Plane  Table  Manual  to  make  a  new  arrangement  of  the  "Three-point  problem,"  with  the  intention 
of  simplifying  the  description  of  the  conditions  found  in  practice  and  the  several  steps  required  for 
the  graphic  solution  of  the  problem  with  the  plane  table  according  to  Lehman's  method.  This 
method  is  the  most  rapid  one,  in  the  hands  of  an  experienced  topographer,  but  for  those  who  may 
have  only  occasional  use  for  a  graphic  solution  Bessels's  method  or  the  tracing  paper  protractor 
method  is  recommended. 

295 


296  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

INSTRUMENTS  AND  ADJUSTMENTS. 
THE  PLANE  TABLE. 

The  principal  instrument  in  use  by  the  Coast  and  Geodetic  Survey  for  mapping 
details  is  the  plane  table.  For  this  purpose  it  is  a  universal  instrument.  All  the  neces- 
sary operations  for  producing  a  map  are  executed  with  it  in  the  field  directly  from  the 
country  as  a  model. 

Other  instruments  are  employed  as  auxiliaries  to  it  under  certain  conditions,  as  will 
be  seen  later  on  under  the  head  of  "  Field  practice,"  but  in  general  it  fulfills  all  require- 
ments alone. 

Description  (Illustration  i). — The  plane  table  is  composed  of  a  well-seasoned  draw- 
ing board*  about  30 inches  in  length,  24  inches  in  width,  and  three-quarters  of  an  inch 
thick,  with  beveled  or  rounded  edges.  It  is  commonly  made  of  several  pieces  of  white 
pine,  tongued  and  grooved  together,  with  the  grain  running  in  different  directions  to  pre- 
vent warping.  It  is  supported  upon  three  strong  brass  arms,  to  which  it  is  attached  by 
screws  passing  through  them  and  entering  the  underside  of  the  board,  the  three  holes 
for  the  reception  of  the  screws  being  guarded  by  brass  bushings  and  situated  equidistant 
from  each  other  and  from  the  center  of  the  table.  By  means  of  these  screws  the  board 
can  be  removed  at  will. 

The  movements  (Illustrations  i  and  2)  of  the  tables  in  use  by  the  Coast  and 
Geodetic  Survey  are  made  from  several  different  models,  but  as  the  principal  features  are 
the  same  in  all  designs  the  description  of  one  type  will  suffice  for  all. 

The  arms  to  which  the  board  is  fastened  rest  upon  the  sloping  upper  face  of  a 
rather  flat  hollow  cone  of  brass,  to  which  they  are  permanently  fixed.  Upon  its  lower 
edge  or  periphery  this  cone  is  fashioned  into  a  horizontally  projecting  rim,  the  inferior 
face  of  which  is  as  nearly  as  possible  a  perfect  plane,  and  this  in  its  turn  rests  upon  a 
corresponding  rim  of  somewhat  greater  diameter  projecting  slightly  beyond  it.  This 
second  rim  forms  the  upper  and  outer  flange  of  a  circular  metal  disk  in  the  form  of  a 
very  shallow  cylinder.  The  inferior  face  or  plane  of  the  upper  flange  or  rim  has,  at  its 
contact  with  the  superior  face  of  the  lower,  a  horizontal  rotary  movement  about  a 
common  center  which  is  also  the  center  of  the  instrument,  and  the  two  are  held 
together  by  means  of  a  solid  conical  axis  of  brass  extending  upward  from  the  center  of 
the  inner  face  of  the  lower  disk.  A  socket  of  similar  shape  fits  exactly  over  this  axis, 
projecting  downward  from  the  inner  side  of  the  apex  of  the  conical  or  upper  disk.  The 
two  plates  are  held  together  by  means  of  a  screw  with  a  milled  head,  capping  the  cone 
from  the  outside,  and  which  can  be  loosened  or  removed  at  pleasure. 

A  tangent  screw  and  clamp  fastened  to  the  edge  of  the  upper  rim  permit,  when 
loose,  the  revolution  of  the  table  about  its  center,  and,  when  clamped  to  the  lower  limb, 
hold  the  table  firm  while  the  tangent  screw  gives  a  more  delicate  movement. 

Three  equidistant  vertical  projections  of  brass,  grooved  on  the  underside,  and  cast 
in  one  piece  with  the  under  face  of  the  lower  disk,  extending  from  the  periphery  toward 
the  center,  rest  upon  the  points  of  three  large  screws  which  come  through  a  heavy 
wooden  block  below.  This  block,  which  is  the  top  of  the  stand  and  is  approximate  in 
form  to  an  equilateral  triangle,  is  2%  inches  thick  when  made- of  wood. 

*  It  is  contemplated  having  the  board  made  of  a  special  aluminum  alloy. 


NO.  2. 


PLANE  TABLE  MOVEMENT. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  297 

The  three  screws  last  mentioned  have  large  milled  heads,  are  quite  stout,  and  play 
through  the  block  below  by  means  of  brass  female  screws  let  into  it.  They  are  the 
leveling  screws  of  the  instrument  and  are  equidistant  from  its  center. 

Upon  the  underside  and  center  of  the  metal  lower  disk  is  a  socket  containing  a 
ball  with  a  brass  arm,  which  projects  through  the  center  of  the  block  from  beneath. 
The  lower  end  of  the  arm  is  threaded,  and  upon  it  plays  a  female  screw  with  a  large 
milled  head,  which  can  be  relaxed  or  tightened  at  pleasure.  The  screw  clamps  the 
whole  upper  part  of  the  instrument  to  the  stand;  it  is  loosened  only  before  leveling 
and  kept  securely  clamped  at  all  other  times. 

The  block,  made  either  of  wood  or  brass,*  is  supported  upon  three  legs,  and  with 
them  forms  the  tripod  or  stand  of  the  instrument,  the  legs  being  of  such  a  length  as  to 
bring  the  table  to  a  convenient  height  for  working,  and  so  arranged  as  to  be  taken  off 
at  will,  or  closed  so  that  their  brass-shod  and  pointed  ends  can  be  brought  together  or 
moved  outward,  as  may  be  required.  They  are  made  on  the  open  or  skeleton  pattern, 
and  each  is  securely  attached  to  a  segment  of  the  tripod  head  by  a  long  brass  bolt. 

MOUNTAIN   PLANE  TABLE. 

A  small  plane  table,  with  a  board  measuring  only  14  by  17  inches,  is  employed  in 
reconnaissance,  mountain  work,  or  as  an  auxiliary  to  one  of  the  standard  size.  All  the 
various  parts  are  reduced  in  size  to  correspond  with  the  board,  and  the  construction  of 
the  movement  simplified. 

THE  ALIDADE. 

The  type  of  alidade  in  general  use  (Illustration  3)  consists  of  a  skeleton  rule  (12 
inches  long  by  2^  inches  wide)  nickel-plated  underneath,  from  and  perpendicular  to 
which  rises  a  metal  column  (3  inches  high),  surmounted  by  Y's,  receiving  the  trans- 
verse axis  of  the  telescope,  to  one  end  of  which  axis  is  firmly  attached  a  graduated  arc 
of  30°,  each  side  of  a  central  o°,  an  accompanying  vernier  being  attached  to  the  Y 
support.  The  arc  moves  with  the  telescope  as  it  is  raised  or  depressed,  and  it  is  used 
in  the  measurement  of  vertical  angles  to  determine  heights.  A  clamp  and  a  tangent 
screw  placed  on  the  other  side  of  the  telescope,  opposite  the  arc,  controls  its  vertical 
movement. 

The  telescope  is  fitted  accurately  near  its  center  of  gravity  within  a  closely  fitting 
cylinder,  to  which  is  solidly  attached  the  transverse  axis.  The  telescope  revolves  within 
the  cylinder  180°,  stops  being  fitted  for  that  range.  This  affords  an  easy  mode  of 
adjusting  the  cross  lines  to  the  axis  of  revolution,  and  for  correcting  with  a  striding 
level  the  errors  of  level  and  collimation  and  revolution  of  the  telescope. 

Upon  the  tube  of  the  telescope  are  turned  two  shoulders,  on  which  rest  a  striding 
spirit  level,  which  can  be  readily  reversed  or  removed  at  pleasure.  The  eyepiece 
carries  the  usual  reticule  with  screws  for  the  collimation  adjustment,  and  to  this  is 
attached  a  glass  diaphragm,  having  one  vertical  and  three  horizontal  lines  engraved 
upon  it.  One  of  the  horizontal  lines  crosses  the  middle  of  the  diaphragm,  the  other  two 
are  placed  equidistant  from  it,  one  above  and  one  below.  The  interval  between  them 
remains  a  constant  chord  for  the  measurement  of  distance  upon  a  graduated  staff  or  rod. 

*  Now  made  of  a  special  aluminum  alloy. 


298  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

In  some  cases  short  auxiliary  lines  have  been  added  dividing  the  interval  into  still 
smaller  chords. 

Several  of  the  alidades  are  furnished  with  a  micrometer  eyepiece  so  attached  that 
the  thread  is  horizontal,  and  has  a  vertical  movement  for  measuring  the  angular  distance 
of  a  fixed  length  on  a  rod  which  remains  a  constant  chord. 

To  the  rule  of  the  alidade  are  attached  two  spirit  levels,  one  in  the  longitudinal 
direction  of  the  rule  and  the  other  at  right  angles  to  it. 

A  dedinatoire  (shown  in  Illustration  i )  accompanies  the  alidade  and  is  carried  in 
the  same  packing  box.  It  consists  of  a  rectangular  brass  box  7  inches  long  by  2  wide, 
with  an  arc  at  each  end  graduated  to  15°  on  each  side  of  the  o°.  It  contains  a  needle 
long  enough  to  extend  from  arc  to  arc,  and  resting  on  a  pivot  midway  the  box.  The 
sides  running  lengthwise  the  box  are  parallel  to  a  line  connecting  the  zero  marks  of 
the  two  arcs. 

The  metal  clamps,  for  holding  the  projection  on  the  board,  are  of  two  kinds: 
U-shaped  for  the  ends,  and  the  side  clamps,  the  latter  being  made  of  thin  metal  strips 
about  12  inches  in  length,  with  two  or  more  springs  attached  to  grip  the  underside  of 
the  board. 

Adjustments. — From  the  nature  of  the  service  in  some  sections  of  the  country  the 
plane  table  is  often  necessarily  subjected  to  rough  usage,  and  there  is  a  constant  liability 
to  a  disturbance  of  the  adjustments;  still,  in  careful  hands,  a  well-made  instrument  may 
be  used  under  very  unfavorable  conditions  for  a  long  time  without  being  perceptibly 
affected.  One  should  not  fail,  however,  to  make  occasional  examinations,  and  while  at 
work,  if  any  difficulty  be  encountered  which  can  not  otherwise  be  accounted  for,  it 
should  lead  directly  to  an  examination  of  the  adjustments. 

1.  The  fiducial  edge  of  the  rule. — This  should  be  a  true  straight  edge.     Place  the 
rule  upon  a  smooth  surface  and  draw  a  line  along  the  edge,  marking  also  the  lines  at 
the  ends  of  the  rule.     Reverse  the  rule  and  place  the  opposite  ends  upon  the  marked 
points  and  again  draw  the  line.     If  the  two  lines  coincide  no  adjustment  is  necessary; 
if  not,  the  edge  must  be  made  true. 

There  is  one  deviation  from  a  straight  line,  which,  by  a  very  rare  possibility,  the 
edge  of  the  ruler  might  assume,  and  yet  not  be  shown  by  the  above  test;  it  is  when  a 
part  is  convex  and  a  part  similarly  situated  at  the  other  end  concave,  in  exactly  the  same 
degree  and  proportion.  In  this  case,  on  reversal,  a  line  drawn  along  the  edge  of  the 
rule  would  be  coincident  with  the  other,  though  not  a  true  right  line;  this  can  be  tested 
by  a  true  straight  edge. 

2.  The  levels  attached  to  the  rule. — Place  the  instrument  in  the  middle  of  the  table 
and  bring  the  bubble  of  either  level  to  the  center  by  means  of  the  leveling  screws  of  the 
table;  draw  lines  along  the  edge  and  ends  of  the  rule  upon  the  board  to  show  its  exact 
position,  then  reverse  180°.     If  the  bubble  remains  central  it  is  in  adjustment;  if  not, 
correct  it  one-half  by  means  of  the  leveling  screws  of  the  table,  and  the  other  half  by 
the  adjusting  screws  attached  to  the  level.     This  should  be  repeated  until  the  bubble 
keeps  its  central  position  whichever  way  the  rule  may  be  placed  upon  the  table.     This 
presupposes   the  plane  of  the  board   to  be  true.     The  other  level   should   now  be 
examined  and  adjusted  in  a  like  manner. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL. 

Great  care  should  be  exercised  in  manipulation  lest  the  table  be  disturbed. 

3.  Parallax. — Move  the  eyeglass  until  the  cross  hairs  are  perfectly  distinct,  and 
then  direct  the  telescope  to  some  distant  well-defined  object.     If  the  contact  remains 
perfect  when  the  position  of  the  eye  is  changed  in  any  way,  there  is  no  parallax;  but  if 
it  does  not,  then  the  focus  of  the  object  glass  must  be  changed  until  there  is  no  dis- 
placement of  the  contact.     When  this  is  the  case  the  cross  hairs  are  in  the  common 
focus  of  the  object  and  eyeglasses.     It  may  occur  that  the  true  focus  of  the  cross  hairs 
is  not  obtained  at  first,  in  which  case  a  readjustment  is  necessary,  in  order  to  see  both 
them  and  the  object  with  equal  distinctness  and  without  parallax. 

4.  Axis  of  revolution. — Since  the  bearings  of  the  pivots  are  fixed,  the  axis  of 
revolution  is  assumed  to  remain  parallel  to  the  plane  of  the  rule. 

5.  Vertical  line  of  diaphragm. — Point  the   intersection  of   the  vertical  and  the 
middle  horizontal  lines  of  the  diaphragm  on  some  well-defined  distant  object;  revolve 
the  telescope  in  its  collar  180°  and  again  observe  the  object.     If  the  intersection  covers 
it,  the  adjustment  is  perfect;  if  not,  one-half  the  error  must  be  corrected  by  moving 
the  diaphragm,  by  means  of  the  adjusting  screws,  and  the  other  half  with  the  tangent 
screw  of  the  table.     This  operation  should  be  repeated  until  the  adjustment  is  perfect. 

6.  Middle  horizontal  line  of  diaphragm. — (i)  Adjust  the  striding  level  by  reversing 
it  end  for  end  and  correcting  its  error — half  the  difference  by  its  own  adjustment,  half 
by  the  tangent  screw  of  the  telescope. 

(2)  Point  the  telescope  to  a  target,  and  note  the  reading,  or  make  a  mark  where 
the  wire  points,  when  the  bubble  is  in  the  middle. 

(3)  Revolve  the  telescope  in  its  collar  180°,  and  note  the  reading  or  mark  the 
place  where  the  wire  points,  when  the  bubble  is  in  the  middle. 

(4)  The  mean  of  the  two  pointings  is  the  true  level  line,  upon  which  the  wire  is 
to  be  adjusted,  which  may  be  done  in  this  way:  Keep  the  bubble  in  the  middle  and  by 
means  of  the  adjusting  screws  bring  the  middle  wire  to  bisect  a  point  half  way  between 
the  two  readings  or  marks.     The  adjustment  may  be  verified  by  revolving  the  telescope 
as  in  (2)  and  if  the  middle  wire  again  bisects  the  point  the  adjustment  is  perfect. 

(5)  If  it  is  now  desired  to  make  the  vernier  read  zero  on  the  vertical  arc,  the  table 
must  be  carefully  leveled;  and  in  order  to  do  this  more  perfectly  than  can  be  done  with 
the  levels  on  the  ruler,  it  may  be  done  by  observing  the  striding  level;  the  telescope 
remaining  clamped,  the  striding  level  should  read  the  same  in  every  position  of  the 
alidate  when  the  table  is  perfectly  level.     (In  general,  this  will  be  found  too  delicate  a 
test,  as  the  table  is  not  sufficiently  even  for  so  sensitive  a  level  to  be  employed. )     The 
table  being  leveled,  move  the  telescope  with  the  tangent  screw  until  the  bubble  is  in 
the  middle,  and  then  set  the  vernier  to  read  zero;  the  screw  holes  in  it  are  oblong,  so 
that  it  admits  of  being  pushed  either  way. 

(6)  It  is  easy  to  have  the  adjustments  near  enough  to  serve  for  running  curves  of 
equal  elevation,  but  in  determining  the  heights  of  stations  it  is  best  to  make  the  obser- 
vations complete,  with  reversals,  both  of  level  and  of  telescope,  taking  the  mean  of  the 
observations,  by  which  the  errors   of  adjustment  are  eliminated.     This,  in   fact,  is 
always  done  with  the  theodolite,  and  should  be  done  with  the  alidade  when  precision 
is  required. 


^00  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

The  following  may  serve  as  an  example: 

TELESCOPE  DIRECT. 

Reading  of  vernier,  level  direct  with  bubble  in  center 4-  o°  '  i' 

Reading  of  vernier,  level  reversed  with  bubble  in  center o' 


Mean +  o°     o'.$ 

Station,  reading -f-  2°  17' 


Angle  of  elevation  (difference) 2°  i6/.5 

TELESCOPE  INVERTED. 

Reading  of  vernier,  level  direct  with  bubble  in  center —  o°     2' 

Reading  of  vernier,  level  reversed  with  bubble  in  center -  V 


Mean —  o°     i'.s 

Station  . .  +  2°  12' 


Angle  of  elevation  (difference) 2°  13'. 5 


Mean 2°  15' 

It  will  be  seen,  from  analyzing  these  observations,  that  the  level  was  one-half 
minute  out  of  adjustment,  the  horizontal  wire  one  and  one-half  minutes,  and  that 
revolving  the  telescope  in  its  collar  180°  changed  its  relation  to  the  index  on  the 
vernier  by  i'.  The  mean  is  free  from  all  errors  of  adjustment. 

The  stadia  rod*  (Illustration  3),  used  in  the  Coast  and  Geodetic  Survey,  is  simply 
a  scale  of  equal  parts  painted  upon  a  wooden  rod  about  10  feet  long,  4  inches  wide, 
and  i^  inches  thick,  so  graduated  that  the  number  of  divisions  upon  it,  as  seen 
between  the  upper  and  lower  horizontal  wires  of  the  telescope  when  the  rod  is  held  at 
right  angles  to  the  line  of  sight,  is  equal  to  the  number  of  units  in  the  distance  between 
the  instrument  and  the  rod. 

Graduation. — In  all  cases  the  rod  should  be  graduated  for  the  particular  instru- 
ment, and,  if  the  best  results  are  to  be  obtained,  to  suit  the  convenience  of  the 
observer. 

In  practice  the  alidade  is  mounted  on  a  stand,  and  its  center  is  plumbed  over  one 
end  of  a  hundred-meter  base,  measured  on  level  ground.  A  line,  representing  the  zero 
of  the  graduation,  having  been  drawn  about  5  inches  from  one  end  of  the  rod,  the  latter 
is  held  vertical  at  the  other  end  of  the  base,  zero  mark  upward.  The  observer  at  the 
alidade  then  makes  the  upper  horizontal  line  of  the  diaphragm  coincide  with  the  zero 
and  directs  the  rodsman  by  signals  where  to  draw  a  line  which  coincides  with  the  lower 
horizontal  line.  This  intercepted  space  on  the  rod  is  subdivided  to  read  meters  and 
the  graduation  continued  to  within  a  short  distance  of  the  bottom. 

*For  further  details  of  the  theory  of  stadia  measurements  see:  Elemente  der  Vennessungs- 
Kunde,  Bauernfeind,  1873,  P-  322!  Handbuch  der  Vermessungs-Kunde,  Jordan,  1888,  p.  554;  Theory 
and  Practice  of  Surveying,  Johnson,  1898,  p.  238;  Gillespie's  Higher  Surveying,  Staley,  1897,  p.  311; 
Experimental  Study  of  Field  Methods,  Smith,  Bulletin  of  University  of  Wisconsin,  Engineering 
series,  Vol.  I,  No.  5. 


NO.  4. 


UAU 


u 


a 


8 


STADIA  RODS. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  3Ol 

This  graduation  is  represented  by  the  equation 


where  </=the  distance  from  the  center  of  instrument  to  rod  (in  this  case  100  meters); 
/=the  focal  length  of  the  telescope  (which  is  35cm  for  the  average  alidade); 
z=the  distance  between  the  upper  and  lower  wires  of  the  diaphragm  (4mm); 
.y=the  length  of  the  intercepted  portion  of  the  rod  (im.i85); 

<:=the  distance  from  object  glass  to  center  of  instrument  (  =—  J 

As  indicated  in  the  preceding  equation,  the  readings  of  a  rod  graduated  in  this 
manner  are  not  quite  true  for  distances  above  or  below  100  meters,  since  the  vertices  of 
the  constant  and  similar  angles  (.one  subtending  the  chord  represented  by  the  inter- 
cepted space  on  the  rod  and  the  other  by  the  space  between  the  upper  and  lower  wires) 
do  not  lie  at  the  center  of  the  instrument,  but  at  a  distance  beyond  the  object  glass 
equal  to  the  focal  length  of  the  telescope,  and  therefore  the  intercept  on  the  rod  will  not 
be  proportional  for  all  distances  from  the  center  of  the  instrument.  To  have  it  so,  the 
instrument  should  be  mounted  at  a  distance  back  from  the  end  of  the  base  equal  to  one 
and  a  half  times  the  focal  length  of  the  telescope  (f+c).  To  all  readings  of  a  rod 
graduated  according  to  this  last  method  the  constant  quantity  f-\-c  must  be  added. 

The  correction  for  the  first  method  is  small  and  can  be  ignored  for  mapping  on  a 
scale  of  i  -i  coco  or  smaller. 

The  formula  for  the  correction  is: 


Where  K=  correction  in  meters, 

B— distance  read  on  rod  in  meters, 

.Z?'=length  of  base,  in  meters,  for  which  the  rod  was  graduated. 

The  corrections  for  50,  200,  300,  and  400  meters  are  +0.262,  —0.525,  —1.050, 
— 1.575  meters,  respectively. 

Inclined  sights. — When  the  rod  is  held  at  a  point  above  or  below  the  instrument, 
the  line  of  sight  is  inclined  at  an  angle  with  the  horizon,  and  a  correction  has  to  be 
applied  to  the  reading  to  obtain  the  horizontal  distance.  If  the  rod  is  held  perpendic- 
ular to  the  line  of  sight  the  reduced  distance  is  simply  the  product  of  the  cosine  of  the 
angle  of  inclination  into  the  rod  reading.  If  the  rod  is  held  vertical,  which  is  the  usual 
and  also  the  safest  method,  there' is  an  additional  correction  on  account  of  the  oblique 
view  of  the  rod.  These  corrections  can  be  ignored  in  the  ordinary  work  of  the  Survey; 
that  is,  on  a  scale  of  i-ioooo  or  smaller,  since  for  short  distances  they  are  too  small  to 
plot,  and  when  the  distances  are  long  enough  for  them  to  become  appreciable  they  are 
still  small  as  compared  to  the  uncertainty  of  the  rod  reading. 

For  the  convenience  of  the  topographer  engaged  on  large  scale  work,  tables  for 
reducing  readings  of  inclined  sights  can  be  found  at  the  end  of  the  Manual. 

Micrometer  eyepiece. — When  a  micrometer  eyepiece  is  used  in  place  of  the  stadia 
lines,  a  rod  about  3.7  meters  in  length  is  employed,  attached  to  which  are  two  targets. 
A  base  is  measured  on  level  ground  and  the  instrument  either  plumbed  over  one  end  or 
back  of  it  a  distance  equal  to  f-\-c,  depending  upon  the  manner  the  rod  is  to  be  held 


302  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

for  an  inclined  sight.  The  rod  is  then  taken  to  one  of  the  subdivisions  of  the  base, 
consisting  of  an  even  multiple  of  the  unit  adopted;  say  100,  200,  or  300  meters,  and  the 
upper  target  being  fixed,  the  lower  target  is  set  and  fixed  so  that  the  angular  measure 
of  the  interval  by  the  micrometer  will  consist  of  an  even  multiple  of  turns  of  the  microm- 
eter screw.  The  rod  is  now  held  at  the  other  subdivisions  of  the  base,  and  the  readings 
tabulated.  A  distance  table  is  then  prepared,  by  interpolation,  for  the  intermediate 
distances. 

Plane-table  sheet, — From  the  standpoint  of  efficiency  the  plane-table  sheet  is  the  least 
satisfactory  portion  of  the  plane-table  equipment.  Owing  to  its  hygrometric  nature  it  is 
very  susceptible  to  atmospheric  changes:  expanding  and  contracting  unceasingly.  This 
would  be  but  an  insignificant  source  of  error  or  annoyance  if  it  were  equal  in  all  direc- 
tions. The  map  or  plan  would  then  simply  change  its  scale,  for  which  an  allowance 
could  readily  be  made.  But  the  objectionable  feature  arises  from  the  unequal  expan- 
sion and  contraction  which  changes  the  relative  distance  and  directions  of  the  points. 
It  has  been  determined  by  experiment  that  strips  cut  longitudinally  from  drawing  paper 
varied  from  10  to  25  per  cent  more  than  strips  cut  transversely  from  the  same  paper. 

Various  substitutes*  have  been  tried,  but  none  have  proved  entirely  satisfactory. 
The  United  States  Geological  Survey,  to  eliminate  this  distortion,  employs  two  sheets 
of  paragon  paper,  the  size  of  the  plane-table  board,  mounted  with  the  grain  at  right 
angles,  and  with  cloth  between  them. 

This  method  is  applicable  to  small  scale  surveys  where  a  sheet  the  size  of  the  table 
board  covers  a  large  area  of  country,  or,  on  the  other  hand,  to  large  scale  cadastral  sur- 
veys where  the  great  amount  of  detail  makes  the  rate  of  progress  slow.  But  for  inter- 
mediate scales  and  an  area  containing  a  moderate  amount  of  detail,  a  longer  sheet  is 
much  more  economical,  because  a  smaller  number  of  points  are  needed  to  keep  the 
work  within  the  control  of  the  triangulation  than  would  be  required  if  it  was  limited 
to  the  size  of  the  table.  A  certain  amount  of  overlapping  work,  of  which  there  is  more 
or  less  at  the  junction  of  the  two  sheets,  would  also  be  avoided. 

The  plane-table  sheet  of  the  Coast  and  Geodetic  Survey  consists  of  a  sheet  of 
Whatman's  cold-pressed,  hand-made  antiquarian  paper,  52  by  30  inches.  It  is  backed 
with  muslin,  which  extends  about  i  inch  beyond  the  edge  of  the  paper  to  protect  it 
from  fraying. 

To  reduce  the  distortion  to  a  minimum  a  sheet  should  be  thoroughly  seasoned 
before  it  is  taken  to  the  field  or  a  projection  laid  down  on  it.  This  is  effected  by 
exposing  it  alternately  to  a  very  damp  and  a  very  dry  atmosphere.  On  testing  a  sheet 
after  a  week  of  such  exposure  it  will  be  found  to  have  much  less  tendency  to  expand  or 
contract  unequally. 

Paper  stored  away,  piled  up  in  stacks,  does  not  properly  season. 

Scale. — The  selection  of  the  scale  to  be  employed  depends  so  much  on  the  char- 
acter of  the  country  to  be  surveyed,  the  amount  of  detail  to  be  included,  and  the  uses 
to  which  the  completed  map  will  be  put,  that  no  general  rule  can  be  given  for  guidance. 
It  must  be  remembered,  however,  that  nothing  is  gained,  either  in  economy  or  rapidity, 
by  the  use  of  small  scales  when  the  details  are  shown  to  be  plentiful.  The  minute 
drawing  involved  proves  a  tax  on  the  topographer  and  is  a  great  time  consumer. 


*Celluloid  sheets  are  frequently  used  in  Alaska.     The  pencil  lines  are  neither  washed  out  nor 
blurred  by  water  accumulating  on  the  sheet. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  303 

The  scale  adopted  by  the  Coast  and  Geodetic  Survey  for  the  coast  line  from  Maine 
to  Delaware  Bay  is  i-ioooo;  from  Delaware  Bay  southward,  1-20000.  Special  surveys 
have  been  made  on  a  scale  as  large  as  1-1200. 

PROJECTIONS   FOR   FIELD   SHEETS. 

It  is  presumed  that  determination  has  been  made,  by  triangulation,  of  points  most 
suitable  for  the  use  of  the  topographer  who  follows  with  the  plane-table  work,  and  that 
a  sketch  of  the  same  is  at  hand,  giving  an  approximate  skeleton  map  of  the  area  to  be 
surveyed.  The  location  or  orientation  (as  it  is  frequently  called)  of  the  sheet  is  then 
based  upon  several  important  considerations. 

It  may  be  taken  as  a  rule  that  the  intervisibility  of  the  points  extends  across  val- 
leys, from  summit  to  summit,  or  across  rivers,  bays,  and  other  bodies  of  water.  So  that 
generally  the  line  of  greatest  depression  of  the  valley  (thalweg)  should  follow  as  nearly 
as  practicable  the  middle  of  the  sheet,  regard  being  had  for  any  abrupt  change  of  direc- 
tion or  importance  of  lateral  features;  or,  in  other  words,  the  areas  to  be  surveyed 
should  be  divided  as  far  as  possible  into  water  basins,  extending  from  divide  to  divide, 
and  not  center  upon  a  ridge  forming  portions  of  two  basins.  The  reason  for  this  being 
that  from  either  slope  of  the  basin  points  are  visible  on  the  opposite  summits  which  will 
be  common  to  the  sheets  which  include  the  adjoining  valleys,  while  from  the  middle  of 
the  valley  points  will  be  visible  on  both  summits. 

From  the  written  descriptions  of  the  points  determined,  discrimination  should  be 
made  in  regard  to  their  temporary  or  permanent  character.  A  flag  in  a  tree  is  likely  to 
have  disappeared  soon  after  its  determination,  and  the  usual  cut  of  a  triangle  in  its  bark 
may  have  disappeared  before  the  lumberman's  ax,  while  a  church  spire,  a  light-house, 
a  house  chimney,  a  copper  bolt  in  a  rock,  or  a  bottle  buried  beneath  the  surface  of  the 
ground  is  more  likely  to  be  recovered  and  to  be  of  service  to  the  topographer. 

Two  intervisible  points,  one  of  which  may  be  occupied,  or  three  inaccessible  points, 
are  all  that  are  absolutely  necessary  upon  a  sheet  for  the  commencement  of  work,  for 
from,  or  upon  these,  all  other  points  required  may  be  determined,  and  it  is  oftener 
more  important,  from  considerations  of  economy  of  time  and  facility  for  work,  to  have 
more  regard  for  embracing  the  topographical  subject  in  its  entirety,  where  points 
may  be  determined  at  convenience,  than  to  furnish  a  large  number  of  determined 
points  at  the  expense  of  the  best  orientation  of  the  sheets  in  regard  to  topographical 
details. 

In  flat  sections  where  the  vertical  question  is  scarcely  a  factor,  the  main  ques- 
tion is  generally  a  plan  that  will  cover  the  area  with  the  fewest  sheets  compatible 
with  a  sufficient  overlap  of  common  points;  and  where  the  object  is  a  survey  of  one  side 
of  a  river  or  other  body  of  water,  points  on  the  opposite  shore  should  be  included  when 
possible. 

When  it  is  possible,  the  sheet  should  be  located  by  one  familiar  with  the  peculiar 
topography  of  the  region  to  be  surveyed,  and  with  some  knowledge  from  observation 
of  the  relative  value  of  the  points  between  which  there  may  be  any  necessity  for 
discrimination. 

Where  the  surface  is  broken  without  any  marked  basins  of  large  area,  and  when 
the  sheet,  on  the  scale  determined  upon,  will  cover  several  successive  basins  and  divid- 

75930°— 15 2 


304  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

ing  ridges,  the  consideration  of  reach  from  higher  to  higher  summits  should  control  as  in 
the  reach  over  one  valley;  thereby  affording  the  best  means  for  determining  position  and 
any  desirable  auxiliary  points  in  the  lower  intermediate  summits  and  in  the  valleys. 

Points  at  the  junction  of  confluent  streams  have  usually  large  arcs  of  visibility,  and 
are  consequently  of  great  value  for  purposes  of  orientation.  If,  therefore,  such  a  point 
should  be  near  but  off  the  edge  of  a  sheet  of  regular  dimensions,  and  from  the  necessi- 
ties at  the  opposite  edge  can  not  be  included  by  it,  it  is  often  well  to  extend  the  length 
of  the  sheet  so  as  to  include  the  point,  even  though  there  may  be  no  intention  to  com- 
plete topographic  details  upon  the  additional  piece. 

Light-houses  are  often  of  this  character,  the  reasons  governing  the  selection  of  their 
positions  for  light  purposes  having  equal  weight  in  the  selection  of  such  positions  for 
survey  signals. 

The  draftsman  will  be  materially  assisted  in  laying  out  the  limits  of  the  projection 
by  drawing  on  a  piece  of  tracing  vellum  a  plan  of  the  sheet,  corresponding  in  size  to  the 
scale  of  the  triangulation  sketch.  Take,  for  example,  a  sheet  52  inches  in  length  by  30 
in  width,  on  which  a  projection  on  a  scale  of  i-ioooo  is  to  be  drawn,  the  triangulation 
sketch  being  on  a  scale  of  i-iooooo.  The  dimensions  of  the  plan  will  then  be  one- 
tenth  those  of  the  sheet,  viz,  5.2  by  3.0  inches.  Placing  the  pattern  over  the  sketch 
and  shifting  its  position  about  over  the  locality  to  be  surveyed,  the  limits  which  include 
the  most  favorable  conditions  for  the  projection  will  soon  become  apparent. 

The  Poly  conic  projection  *  has  been  adopted  by  the  Coast  and  Geodetic  Survey  for 
mapping  its  work.  The  method  of  constructing  one  is  as  follows: 

The  limits  of  the  sheet  having  been  determined,  the  middle  meridian  A  (see  illus- 
tration 5)  is  located  and  drawn;  then  its  intersection  with  the  most  central  parallel  is 
found,  and  the  perpendicular  B  erected  there. 

Next  turn  to  the  page  of  the  "Tables  for  a  polyconic  projection  of  maps"f  in 
which  is  given  the  degree  of  latitude  which  includes  the  limits  of  the  sheet.  In  this 
instance  the  latitude  is  40°,  to  be  found  on  page  223  of  the  tables.  The  number  of  min- 
utes of  latitude  on  the  central  meridian,  above  and  below  the  central  parallel,  being 
known,  take  the  corresponding  distance  from  the  column  headed  "Sums  of  minutes  for 
middle  latitude"  and  lay  it  off  (C)  above  and  below  the  central  parallel,  and  with  the 
same  distance  as  radius,  strike  arcs  D  D  D  D  above  and  below,  from  near  the  extremi- 
ties of  the  perpendicular  B.  With  a  well-tested  straightedge  draw  lines  E  E  through 
the  north  and  south  minutes  on  the  central  meridian,  and  tangent  to  the  two  arcs  D  D 
to  the  right  and  left.  This  gives  three  parallel  lines  perpendicular  to  the  central  merid- 
ian. On  the  opposite  page  222,  from  under  the  head  of  '  'Arcs  of  the  parallel  in  meters, ' ' 
take  out  the  value  corresponding  to  the  number  of  minutes  of  longitude  east  and  west 
of  the  central  meridian  and  lay  off  the  whole  distance  F  F'  F"  on  each  perpendicular, 
taking  each  distance  from  its  appropriate  latitude.  Subdivide  these  into  minutes 
G  G'  G". 

For  the  areas  usually  covered  by  plane-table  sheets  the  corrections  X,  for  deter- 
mining the  abscissas  from  the  arcs  of  parallels  (Table  VI,  head  "  Coordinates  of  curv- 

*  See  a  Treatise  on  Projections,  Craig,  United  States  Coast  and  Geodetic  Survey  1882.     Chart 
and  Chart  Making,  Pillsbury,  No.  29,  Proceedings  United  States  Naval  Institute, 
t  United  States  Coast  and  Geodetic  Survey  Special  Publication  No.  5,  1900. 


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APPENDIX  7.     A  PLANE  TABLE  MANUAL.  305 

ature"  ),  are  inappreciable  and  may  be  disregarded,  the  ordinates  Y  only  being  used. 
These  give  the  distances  to  be  set  off  from  the  lines  B  and  E,  perpendicularly  toward  the 
pole,  for  each  minute  of  longitude  counting  from  the  central  meridian.  For  ordinary 
field  projections  of  scale  i-ioooo  the  ordinateof  the  extreme  minute  only  need  be  used, 
and  the  parallel  drawn  a  right  line  from  the  point  so  found  to  the  central  meridian. 
This  ordinate  H  being  set  off  on  each  of  the  parallels,  the  meridians  are  all  drawn  in 
with  a  fine  ruling  pen,  then  subdivided  into  minutes,  and  the  parallels  carefully  ruled 
in  through  the  points  of  subdivision. 

The  projection  is  verified  by  applying  the  measure  of  a  number  of  minutes  of  lati- 
tude and  longitude,  and  by  a  comparison  of  diagonal  measurements  on  different  parts 
of  the  sheet. 

All  measurements  should  be  carefully  taken  from  the  scale  with  a  keenly  pointed 
beam-compass,  and  the  marks  pricked  in  the  paper  should  be  as  light  as  possible  to  be 
seen,  so  as  to  insure  the  greatest  possible  accuracy. 

The  draftsman  is  supplied  with  a  list  of  triangulation  points,  which  gives  their  rel- 
ative distances,  their  latitudes  and  longitudes,  and  also  the  equivalents  in  meters  of  the 
seconds  of  latitude  and  longitude,  according  to  which  the  points  are  now  plotted  on  the 
sheet  by  measuring  from  the  corresponding  minutes.  Thus  in  the  diagram  the  distance 
J  represents  the  seconds  of  latitude;  K,  the  seconds  of  longitude  of  the  trigonometric 
point. 

The  accuracy  of  the  plotting  is  tested  by  a  measurement  of  the  respective  dis- 
tances between  the  points  with  a  beam-compass,  these  distances  being  also  given.  The 
latitude  and  longitude  are  then  plainly  marked,  usually  on  the  north  and  east  sides  of 
the  sheet,  at  one  extremity  of  each  parallel  and  meridian,  and  the  pencil  marks  erased. 

It  sometimes  becomes  necessary  to  base  topographic  work  upon  a  detached  scheme 
of  triangulation,  before  the  usual  astronomic  observations  have  been  made.  In  this 
case  the  only  elements  given  are  the  distances  from  the  points  to  two  projected  arcs  of 
rectangular  coordinates  (which  are  assumed)  and  the  distances  between  the  points. 
The  projection  for  plotting  these  consists  simply  of  axes  of  ordinates  and  abscissas  so 
laid  on  the  sheet  that  it  will  embrace  all  the  points  required  by  the  surveyor,  and  in  the 
manner  most  convenient  for  his  work;  and  the  points  are  plotted  from  these  by  the 
intersection  of  two  arcs  with  the  distances  of  the  points  from  the  axes  as  radii,  either 
north  or  south,  east  or  west  of  the  axes,  as  the  plus  or  minus  sign  given  may  indicate. 
The  only  test  is  by  the  distances  between  the  points,  and  there  should  be  at  least  two 
from  each.  If  the  work  be  correctly  done,  a  regular  projection  can  be  constructed  on 
the  sheet  after  it  is  finished  and  the  required  astronomic  work  is  completed. 

In  case  it  so  happens  that  for  some  special  purpose  it  becomes  urgent  to  undertake 
a  piece  of  topography,  when  neither  the  data  for  projections  nor  coordinates  are  at 
hand,  plotting  by  distances  is  the  only  resource  left,  and,  of  course,  great  care  is 
necessary. 

When  a  sheet  has  no  projection — that  is,  no  meridians  and  parallels,  it  is  advisable 
to  draw  squares  of  i  ooo  or  any  specified  number  of  meters  on  it,  by  means  of  which 
the  projection  can  ultimately  be  laid  down  correctly. 

Accessories. — The  usual  accessories  for  plane-table  work  are:  Large  umbrella  for 
shading  table,  binocular,  pocket  compass,  10  or  20  meter  steel  tape,  Locke's  level, 


306  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

clinometer,  metal  scale,  dividers,  pencils,  rubber,  block  of  emory  or  sand  paper,  table 
of  heights,  note,  and  sketch  book.* 

A  metal  chart  case  should  always  accompany  the  table  to  secure  the  sheet  from 
sudden  rain  and  other  injury  liable  to  occur  in  transportation  of  the  sheet  to  and  from 
the  field  and  for  its  safe-keeping  when  not  in  use.  Its  diameter  should  not  be  less  than 
3  inches,  for  no  sheet  can  be  rolled  to  a  less  diameter  without  serious  rupture  of  the 
fiber  of  the  paper.  It  is  also  advisable  to  have  a  rubber  cloth  for  covering  the  table 
when  it  is  carried  from  station  to  station. 

Approximate  weights. — Plane-table  movement,  i8}4  pounds,  boxed,  34^  pounds; 
plane-table  board,  8^  pounds,  boxed,  26^  pounds;  plane-table  alidade,  7  pounds, 
boxed,  21^  pounds;  plane-table  tripod  legs,  n  pounds;  2  stadia  rods,  16%  pounds. 
Mountain  plane  table,  set  up  complete  with  alidade,  19^  pounds,  boxed,  36  pounds; 
2  stadia  rods,  12^  pounds. 

FIELD  WORK. 

Organization  of  party. — In  organizing  a  party  for  field  work  it  is  necessary  to  have 
one  man  to  carry  the  table.  His  duty  is  to  remain  constantly  with  the  instrument, 
never  to  leave  it  unguarded ;  and  while  the  topographer  is  at  work  he  holds  the  umbrella 
to  shade  the  table  from  the  sun  and  thus  protect  the  observer's  eyes  from  the  glaring 
reflections  from  the  paper  and  instruments.  The  table  bearer  should  be  taught  at  the 
beginning  of  the  work  the  mode  of  setting  the  table  over  a  point  and  taking  it  up  from 
the  same.  In  the  first  instance  to  grasp  firmly  two  legs  of  the  tripod  and  with  the 
knee  to  extend  the  third  one  until  it  reaches  the  ground  at  the  proper  distance  from  the 
point,  and  then  place  the  other  two  in  position.  The  distances  from  the  point  will 
vary,  as  the  ground  may  be  level  or  sloping,  in  order  to  keep  the  tripod  head  vertically 
over  the  point  and  approximately  horizontal,  securing  the  latter  condition  by  sighting 
over  the  head  to  the  horizon.  In  taking  up  the  table  two  legs  should  be  grasped 
firmly  and  the  table  raised,  resting  upon  the  other  leg,  upon  which  the  first  two  are 
closed,  when  the  table  is  raised  in  place  upon  the  shoulder. 

Two  rodsmen  are  needed,  and  the  rapidity  with  which  the  work  is  executed  largely 
depends  upon  their  efficiency.  When  well  trained  they  should  be  able  to  recognize  the 
salient  points  of  the  features  to  be  mapped,  so  that  the  topographer  can  draw  in  correctly 
the  details  from  the  least  number  of  readings,  in  the  absence  of  an  aid  to  make  a  sketch 
of  the  intricate  portions. 

The  amount  of  assistance  an  aid  can  give  to  his  chief  is  limited  only  by  his  skill 
and  experience.  The  logical  inference  being  that  he  is  in  training  to  become  a  topog- 
rapher himself,  he  takes  charge  of  an  increasing  share  of  the  work  as  he  becomes  more 
and  more  familiar  with  the  methods  employed.  This  enables  his  chief  to  turn  his  atten- 
tion in  other  directions,  which  will  expedite  the  survey  and  increase  the  output. 

An  outline,  merely,  of  his  duties  can  be  suggested:  Building  signals,  drawing  plans 
of  intricate  details,  sketching  contours,  selecting  stations  in  advance,  running  traverse 
lines  with  auxiliary  instruments,  and  finally  in  taking  charge  of  the  plane  table  in  the 
absence  of  his  chief,  who  is  thus  afforded  the  opportunity  of  inspecting  some  difficult 
area  and  formulating  some  plan  to  meet  the  conditions  found  there. 

*For  the  Locke's  level,  clinometer,  and  pocket  compass  a  Casella  pocket  alt-azimuth  instrument 
may  be  substituted,  as  it  combines  all  three  in  a  very  convenient  form. 


NO.  6. 


iChitnney 


Fig.l 


Fig.  2 


Fig.  3 


cxi 


GRAPHIC  TRIANQULATION. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  307 

The  additional  number  of  men  required  to  complete  the  party  will  depend  mainly 
on  the  means  of  transportation — wagon,  horseback,  or  boat. 

Preliminary  reconnaissance. — Before  commencing  the  instrumental  work,  a  recon- 
naissance of  the  country  should  be  made  for  the  purpose  of  recovering  triangulation 
stations  and  to  locate  signals  at  suitable  points  for  subsequent  determination  and  use. 
In  the  location  of  signals,  either  as  permanent  points  or  simply  for  temporary  forward 
lines,  a  great  deal  depends  upon  the  good  judgment  of  the  person  placing  them.  Two 
purposes  are  to  be  subserved:  First,  the  seeing  of  sufficient  known  points  to  give  a  good 
determination;  and,  second,  to  command  a  view  of  as  great  an  area  of  country,  and  as 
many  natural  and  artificial  features  for  filling  in  the  topography,  as  possible.  It  should 
be  remarked,  also,  that  in  the  course  of  prosecution  of  the  regular  work  no  favorable 
opportunity  must  be  allowed  to  pass  for  locating  a  signal  or  determining  a  point  which 
may  at  some  future  time  be  of  service.  Advantage  should  be  taken  of  open  places  in 
the  woods  commanding  roads  or  ravines.  Piers  or  draws  of  bridges,  or  piles,  giving  lines 
up  and  down  streams,  which  have  precipitous  and  wooded  banks;  trees  of  unusual 
appearance  in  prominent  positions,  or  bearing  flags  placed  upon  them  for  the  purpose; 
points  of  rock,  offshore  or  otherwise;  lightning  rods,  cupolas,  weathercocks,  chimneys 
of  factories,  and  other  peculiar  and  marked  objects  come  within  this  category.  In  fact, 
it  may  be  set  down  as  a  rule  that  well-determined  signals  located  at  convenient  distances 
over  the  sheet  are  more  likely  to  be  too  few  than  too  many. 

Signal  poles  should  be  straight  and  perpendicular,  and  the  flags  upon  them  adapted 
in  color  to  the  background  against  which  they  will  be  seen  when  observed  upon. 

Graphic  triangulation  (Illustration  6). — Signals  having  been  erected  at  each  trian- 
gulation station,  and  also  on  all  prominent  hills  within  the  area  of  the  sheet,  where  they 
will  be  useful  in  providing  additional  control,  the  next  proceeding  will  be  to  occupy 
one  of  the  former  points. 

Care  should  be  exercised  in  choosing  a  day  for  this  portion  of  the  work,  as  it  is 
essential  to  have  favorable  weather  for  a  satisfactory  test  of  the  plotted  points  in  the 
field  and  for  the  determination  of  new  ones. 

On  arrival  at  the  station  the  table  is  set  up  approximately  over  the  center  mark, 
and  the  sheet  secured  to  the  table,  so  that  it  will  be  held  firmly  and  evenly  and  not  be 
disturbed  in  its  position  by  the  friction  of  the  alidade,  nor  by  ordinary  winds.  As  the 
longest  side  of  the  board  is  usually  made  equal  to  the  width  of  the  sheet,  and  the  sheet 
is  usually  longer  than  this  width,  the  excess  of  length  is  rolled  up  inward,  turned  under- 
neath the  sides  <$f  the  table  and  fastened  with  a  metal  spring  clamp,  biting  from  the  top 
of  the  sheet  on  the  table  to  the  inside  of  the  roll  beneath.  One  clamp  at  each  end  of 
the  roll  serves  to  hold  the  roll  ends  securely.  The  sides  of  the  sheet  are  sometimes  held 
to  the  table  by  similar  but  shorter  clamps,  but  it  is  preferable  for  the  free  movement  of 
the  alidade,  and  more  secure  against  strong  winds,  that  a  metal  strip,  the  length  of  the 
side  between  the  end  clamps,  with  spring  clamps  fastened  to  the  outer  edge,  and  biting 
the  underside  of  the  table,  be  used  for  holding  down  the  edges  of  the  paper. 

The  chief  and  controlling  condition  in  work  with  the  plane  table,  and  without  which 
no  accurate  work  can  be  done,  is  that  the  table  shall  be  oriented — that  is,  that  all  lines 
joining  points  on  the  sheet  shall  be  parallel  to  the  corresponding  lines  of  nature. 

Let  T,  T',  T",  T'"  (Fig.  i)  represent  the  board  of  the  plane  table,  upon  which  is 
spread  the  sheet;  the  plotted  triangulation  point  a  upon  the  sheet  representing  the 


308  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

signal  A  upon  the  ground;  b,  the  spire  B;  c,  the  signal  C;  and  p,  the  station  P;  the 
small  letters  on  the  sheet  representing  the  centers  of  the  signals  on  the  ground,  which 
are  referred  to  by  corresponding  capital  letters. 

The  table  is  placed  approximately  level  over  the  station  occupied,  P,  and  oriented,  also 
approximately,  by  the  eye,  so  that  the  plotted  points  on  the  sheet  are  in  approximate 
range  with  the  station  P  and  the  signals  or  objects  they  represent  in  the  field.  Then 
plumb  the  point  p  over  the  station  P,  fixing  the  legs  of  the  table  firmly  in  the  ground. 

In  maps  of  large  scale  it  is  important  to  plumb  the  plotted  point  exactly  over  the 
station,  but  on  the  usual  field  scales  of  the  Coast  and  Geodetic  Survey  (i-ioooo  and 
1-20000)  an  approximation  with  the  eye  is  all  that  is  requisite.  To  effect  it  more 
closely  a  small  stone  is  held  underneath  the  point  and  then  dropped  to  test  the  position, 
or  a  plumb  bob  fastened  to  the  table  below  the  point  serves  the  same  purpose.  Plumb- 
ing arms  or  forks  are  made  and  supplied  by  the  instrument  dealers. 

The  plotted  point  having  been  plumbed  over  the  station  as  accurately  as  the  scale 
of  the  work  demands,  place  the  alidade  on  the  table  so  that  the  rule  shall  extend  across 
and  parallel  with  the  line  joining  two  of  the  leveling  screws;  loosen  the  large  clamp  screw 
under  the  tripod  head,  and  with  the  leveling  screws  bring  the  bubbles  of  the  two  levels 
on  the  rule  to  the  center;  clamp  the  screw  under  the  tripod  head,  and  the  table  is  level. 
Now,  unclamp  the  revolving  plate,  place  the  edge  of  the  rule  upon  the  plotted  points  p 
and  b,  the  telescope  being  directed  toward  the  spire  B,  as  shown  by  the  arrow-head  of 
the  figure,  and  revolve  the  table  until  B  is  seen  in  the  field  of  the  telescope;  clamp  the 
revolving  plate,  and  with  the  tangent  screw  of  the  movements  bisect  the  top  or  center 
of  the  spire  B  with  the  vertical  wire  of  the  telescope.  The  table  is  now  oriented,  if  the 
points  have  been  correctly  plotted  and  the  proper  objects  sighted.  To  verify  this,  place 
the  rule  upon  the  point  p  again,  and  upon  the  points  a  and  c,  consecutively,  and  if  the 
two  signals  A  and  C  are  bisected  by  the  vertical  wire  of -the  telescope,  the  position  is 
assured,  and  the  lines  connecting  points  of  the  sheet  are  parallel  with  the  corresponding 
lines  on  the  ground. 

The  failure  to  bisect  A  and  C  would  indicate  an  error  of  plotting  or  an  unequal 
change  of  the  dimensions  of  the  paper  (distortion),  which  must  be  examined,  and  in 
case  of  the  former,  corrected,  and  in  case  of  the  latter,  allowance  made  for,  as  indicated 
later  on.  (See  distortion  errors,  page  316.) 

The  next  proceeding  is  to  draw  the  line  to  the  next  point  which  it  is  desirable  to 
occupy  or  determine,  either  some  natural  object  which  can  be  occupied,  or  a  temporary 
signal  placed  for  that  purpose,  as  the  signal  D. 

The  edge  of  the  rule  is  placed  upon  the  point  /,  and  moved  about  that  point  as  a 
center  until  the  signal  D  is  bisected  by  the  vertical  wire,  and  then  a  line,  /,  is  drawn 
along  the  edge  of  the  rule  from  p  far  enough  to  reach  the  estimated  position  on  the  sheet 
of  the  point  d,  and  at  each  end  of  the  rule  the  short  check  lines  n  n  are  drawn.  These 
check  lines  can  be  used  in  reversing  the  alidade  with  the  accuracy  that  is  obtained  by 
the  greatest  length  of  a  range  line.  They  may  be  indicated  on  the  sheet,  with  names 
of  objects,  as  in  fig.  2 — ch.,  chimney;  /.,  tree;  cup.,  cupola;  sp.,  spire;  w.  m.}  windmill; 
or  numbered,  and  a  record  kept  of  the  objects  sighted,  where  details  are  complex. 

In  the  same  manner  lines  should  be  drawn  to  such  objects  as  it  is  desired  to  deter- 
mine. This  determines  only  the  one  element  of  direction;  it  will  be  necessary  to 
determine  the  distance  from  the  point  occupied  either  by  measurement  or  by  intersec- 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  309 

tion  from  some  other  fixed  point,  at  an  angle  not  less  than  30°  nor  more  than  150°; 
all  acute  intersections  should  be  verified  by  a  direction  from  a  third  point. 

The  table  is  moved  to  the  station  A  (Fig.  2)  and  placed  over  the  point,  oriented 
approximately,  leveled,  and  the  axis  of  revolution  clamped  as  at  station  P.  The  rule 
is  then  set  upon  the  line  a  p,  the  telescope  directed  toward  the  signal  P,  and  the  table 
put  in  position  in  the  manner  described.  Then,  keeping  the  edge  of  the  rule  upon 
a,  direct  the  telescope  to  the  signal  D  and  draw  the  line  a  d,  intersecting  f,  and  deter- 
mining the  position  of  the  point  d  upon  the  sheet,  corresponding  to  D,  and  bearing  the 
same  relation  in  directions  and  distances  from  the  points  p,  a,  6,  and  c  as  the  signal  D 
does  from  P,  A,  B,  and  C.  All  lines  to  other  objects  which  were  drawn  from  p,  and 
which  objects  can  be  seen  from  A,  are  intersected  and  determined  in  the  same  manner. 

When  a  direction  has  been  drawn  from  a  station  to  any  undetermined  point  that 
may  be  occupied,  the  position  of  the  point  may  be  determined  by  occupying  it  with  the 
table,  and  orienting  the  table  by  the  line  drawn  to  it,  and  resecting  upon  a  signal  whose 
corresponding  point  is  plotted  upon  the  sheet. 

The  table  is  placed  over  the  point  D  (Fig.  3),  oriented  approximately,  leveled, 
etc.,  as  at  the  previous  stations.  The  edge  of  the  rule  is  then  placed  upon  the  line  dp, 
passing  through  the  point  p,  so  that  the  checks  n  n  are  just  visible  along  the  edge,  and 
the  telescope  directed  toward  the  signal  P,  and  the  table  oriented.  The  rule  is  then 
placed  with  its  edge  bisecting  one  of  the  plotted  points,  such  as  b,  which  will  give  a  good 
intersection  (the  nearer  90°  the  better)  with  the  line  /,  and  is  moved  about  that  point 
as  a  center  until  the  spire  B  is  bisected  by  the  vertical  web.  A  line  is  now  drawn  accu- 
rately along  the  edge  of  the  rule  through  b,  crossing  the  line/".  If  this  line  intersects  the 
line  /  at  the  point  d,  the  position  of  the  latter  is  assured,  and  a  delicate  hole  with  the 
dividers  should  be  pricked  at  the  point,  surrounded  by  a  small  circle  in  pencil. 

Resection  upon  any  other  determined  point  will  verify  its  position. 

From  this  point,  d,  directions  are  observed  and  drawn  to  verify  the  previous  inter- 
sections upon  chimney,  tree,  cupola,  windmill,  etc. 

There  are  occasions  when  occupying  some  station  that  several  objects  are  seen 
whose  position  it  is  desirable  to  determine  by  prosection,  but  there  is  doubt  of  their  being 
recognized  from  other  stations.  A  new  station  is  then  occupied  close  by  the  first  one 
and  new  lines  drawn  to  the  objects.  The  intersection  thus  obtained  will  necessarily  be 
acute,  but  will  materially  assist  in  their  identification  from  other  localities. 

All  lines  should  be  drawn  lightly  and  carefully,  close  to  the  edge  of  the  rule,  with 
a  hard,  finely-sharpened  pencil.  If  the  table  and  alidade  be  in  proper  condition,  the 
contact  of  the  edge  of  the  rule  with  the  paper  will  be  perfect  throughout  its  length, 
and  in  drawing  a  line  along  the  edge  care  must  be  taken  to  preserve  the  same  inclination 
of  the  pencil  and  to  keep  it  sharp.  If  the  rule  should  be  raised  from  the  paper  at  any 
part,  great  care  is  to  be  observed  that  the  pencil  does  not  run  under  the  edge  and  thus 
deviate  from  a  straight  line. 

Amount  of  control. — There  is  no  fixed  ratio  between  the  number  of  determined 
points  and  the  number  of  square  miles  of  the  region  to  be  surveyed  or  square  inches  of 
plane-table  sheet. 

The  greater  the  number  of  points  well  distributed  over  the  latter  the  less  likelihood 
of  error  due  to  distortion  of  the  paper. 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

A  large  number  also  makes  it  easy  for  the  topographer  to  determine  by  resection 
subordinate  stations  for  mapping  the  details,  and  in  consequence  fewer  traverse  lines 
need  be  run. 

More  than  sufficient  for  these  purposes  are  not  necessary,  and  it  is  important  when 
carrying  on  a  graphic  triangulation  not  to  waste  valuable  time  and  favorable  weather, 
but  to  advance  this  part  of  the  work  as  rapidly  as  possible  before  the  sheet  becomes 
affected  by  exposure. 

The  three-point  problem  (Illustration  7). — A  subordinate  station  is  located  at  any 
desired  place  where  a  good  view  of  the  surrounding  features  can  be  obtained.  If  the 
position  of  this  point  has  not  been  previously  determined  it  is  now  effected  by  means 
of  the  resection  of  lines  from  three  fixed  points. 

The  special  advantages  of  the  plane  table  as  a  mapping  instrument  are  due  to  the 
rapidity  with  which  it  obtains  results  by  the  method  of  graphic  triangulation  and  .to 
the  facility  it  affords  the  topographer  in  determining  his  position  at  an  unknown  point 
by  the  graphic  solution  of  the  three-point  problem. 

When  the  latter  method  is  applicable — that  is,  when  the  country  is  open  and  signals 
can  be  easily  seen — its  superiority  over  a  system  of  traverse  lines  is  manifest.  The 
topographer  is  then  at  liberty  to  choose  his  ground  without  reference  to  his  last  station 
or  to  one  succeeding.  He  is  not  tied  down  to  a  backsight  nor  restricted  by  the  condi- 
tions imposed  by  a  foresight.  He  need  not  set  up  his  instrument  on  an  area  barren  of 
detail  nor  cut  his  way  through  obstacles  (bushes,  hedges,  trees)  to  establish  a  station 
at  a  commanding  point  of  view. 

The  number  and  situation  of  the  stations  are  governed  solely  by  the  amount  and 
location  of  the  information  to  be  mapped.  On  the  other  hand,  traverse  stations  are 
chosen  on  account  of  their  visibility,  and  many  of  them  are  of  no  service  whatever 
beyond  carrying  the  line  forward. 

When  the  table  is  imperfectly  oriented,  the  lines  drawn  from  the  three  projected 
points,  when  sighting  on  the  corresponding  actual  points,  will  not  intersect  at  one  point 
unless  all  four  are  on  the  circumference  of  a  circle.  (See  Fig.  3,  Indeterminate  posi- 
tion.) Except  in  this  case,  two  of  the  lines  will  be  parallel,  intersected  by  a  third 
(see  Fig.  4,  Station  on  range  line  between  two  fixed  points,  and  Fig.  2,  Station  on  pro- 
longation of  range  line),  or  they  will  form  a  small  triangle  called  the  triangle  of  error. 
(Figs,  i,  3,  5,  and  6.)  The  solution  of  the  three-point  problem  determines  the  location 
of  the  station  occupied  and  orients  the  table  simultaneously. 

The  relative  positions  of  the  three  fixed  points  with  reference  to  the  new  station  have 
an  important  bearing  on  the  strength  of  its  determination. 

In  the  following  statement  in  regard  to  the  different  groupings  of  points  met  in 
practice,  for  the  sake  of  brevity,  the  term  "  fixed  points  "  will  be  understood  to  mean 
points  already  determined  and  plotted  on  the  sheet;  the  "  great  triangle"  referred  to 
is  one  formed  by  the  three  fixed  points,  and  the  ' '  great  circle ' '  is  the  circle  passing 
through  them. 

When  the  new  station  is  outside  the  great  circle,  the  strength  for  determination  of  a 
position  will  be  weak  when  the  middle  point  as  seen  from  the  new  station  is  the  farthest 
of  the  three  and  the  angles  are  small.  (See  Illustration  7,  Fig.  3.)  If  the  new  sta- 
tion is  located  outside  the  circle,  and  some  distance  below  it,  the  angles  are  small  and  the 
determination  correspondingly  weak. 


NO.  7. 


Point  sought 


Triangle  of  error 


Fig.l 


Indeter- 


terminate 


Point  sought 


Fig.  6 


A 


Point  sought 


i.  2 


c 

-A 


. 

A 


\-rrp- 

A--- 7r:  \    Point  sought 

b  Range  tine        * \ — 


sought 


Fig.  5 


THE  THREE-POINT  PROBLEM. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  3!! 

The  determination  increases  in  strength  for  given  angles  as  the  middle  point 
approaches  the  new  station.  (Fig.  i.) 

When  one  angle  is  small  or  o°  (points  in  range),  the  determination  will  be  strong, 
provided  the  two  points  making  the  small  angle  or  range  are  not  too  near  each  other 
when  compared  to  the  distances  to  the  new  station  and  to  the  third  point;  provided  also 
the  angle  to  the  third  point  is  not  too  small.  (Fig.  2.) 

When  the  new^stationjiei^on  or^ n^a^jhj_^rjza^drcj,e,  its_positiott  _ia_  in4eternjinate. 
(See  Illustration  7,  Fig.  3.) 

When  the  new  station  is  mithin  the  great  circle,  the  strength  of  its  determination 
increases  as  it  approaches  the  center  of  gravity  of  the  great  triangle.  (Figs.  3,  4,  5.) 

There  are  a  number  of  graphic  solutions,  but  all  save  three  are  better  suited  to  the 
drafting  room  with  its  appliances  than  to  the  conditions  which  exist  in  the  field. 

Lehmann's  method  of  solution  is  the  simplest  and  most  direct,  and  applies  under  all 
circumstances.  The  directions  are  stated  in  the  form  of  rules. 

The  term  '  'point  sought ' '  will  be  understood  to  mean  the  true  position  on  the 
sheet  of  the  projected  point  of  the  station  occupied.  The  surveyor  is  assumed  to  be 
facing  the  signals,  and  the  directions  right  and  left  are  given  accordingly. 

Rule  i. — The  point  sought  is  always  distant  from  each  of  the  three  lines  drawn 
from  the  three  fixed  points  in  proportion  to  the  distances  of  the  corresponding  actual 
points  from  the  station  occupied,*  and  it  will  always  be  found  on  the  corresponding 
side  of  each  of  the  lines  drawn  from  the  fixed  points,  f 

The  simplest  case  for  the  application  of  this  rule  occurs  when  the  station  to  be 
determined  is  within  the  triangle  formed  by  the  three  fixed  points;  the  point  sought 
must  then  be  within  the  triangle  of  error  to  satisfy  the  conditions.  (See  Illustration  7, 

Fig.  50 

Although  Rule  i  is  sufficient  in  itself  for  the  solution  of  the  problem,  there  are  two 
subordinate  rules  which  materially  assist  the  topographer  in  reaching  a  decision  as  to 
the  proper  location  of  the  point  sought  with  reference  to  the  lines  from  the  fixed  points. 

Rule  2. — When  the  point  sought  is  without  the  great  circle  it  is  always  on  the  same 
side  of  the  line  from  the  most  distant  point  as  the  intersection  of  the  other  two  lines. 
(See  Illustration  7,  Fig.  i.) 

Rule  j. — When  the  point  sought  falls  within  either  of  the  three  segments  of  the 
great  circle  formed  by  the  sides  of  the  great  triangle  the  line  drawn  from  the  middle 
point  lies  between  the  point  sought  and  the  intersection  of  the  other  two  lines.  (See 
Illustration  7,  Figs.  3,  4,  6.) 

Application  of  rules. — In  practice  the  topographer  first  decides  the  relation  of  the  new 
station  with  reference  to  the  fixed  points,  whether  it  is  within  the  great  triangle  or  in 
one  of  the  segments  or  outside  the  great  circle.  He  then  determines  the  position  of  the 

*  Demonstration. — A,  B,  C  (Illustration  8,  Fig.  i)  are  projections  of  the  three  signals  from  which 
it  is  desired  to  determine  by  resection  the  position  of  a  fourth  point,  D.  The  table  being  out  of  posi- 
tion to  the  right,  the  triangle  of  error  formed  by  the  three  lines  from  A,  B,  and  C  is  ab,  ac,  be.  The 
true  point  occupied  lies  at  D,  being  at  the  intersection  of  the  circles  AB  ab,  AC  ac,  BC  be.  Now,  if 
perpendiculars  be  drawn  from  D  to  the  lines  drawn  from  A,  B,  and  C,  we  shall  have 

Da  :  Db  ::  DA  :  DB  or  Db  :  DC  ::  DB  :  DC. 

t  That  is,  if  it  is  on  the  right  side  of  one  line,  it  is  on  the  right  side  of  each  one  of  the  other  two, 
and  if  on  the  left  side  of  one,  it  is  on  the  left  side  of  each  one  of  the  other  two. 


312  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

point  sought  with  reference  to  one  line  (if  within  one  of  the  segments  or  without  the 
great  circle  by  Rule  2  or  3);  it  then  follows  from  Rule  i  that  it  must  be  on  the  corre- 
sponding side  of  the  other  two  lines.  Finally,  he  estimates  the  relative  distances  of  the 
three  actual  points  from  him  and  marks  the  position  of  the  point  sought  a  proportionate 
distance  from  the  three  lines. 

EXAMPLES. 

Illustration  7,  Fig.  i:  When  the  point  sought  is  without  the  great  circle,  the  inter- 
section of  the  lines  from  B  and  C  fall  to  the  right  of  the  line  from  A,  the  most  distant 
point;  therefore  (Rule  2)  the  point  sought  must  be  on  its  right,  and  also  (Rule  i)  on 
the  right  of  the  line  from  B  and  C.  Its  exact  position  is  then  estimated  according  to 
Rule  i. 

Illustration  7,  Fig.  2:  When  the  point  sought  is  on  or  near  the  prolongation  of  a 
range  line,  it  must  be  outside  the  parallel  lines  on  the  side  of  the  line  to  the  nearest 
fixed  point  of  the  range.  In  the  figure  it  will  be  seen  that  the  point  sought  must  be 
outside  the  lines  from  A  and  B,  and  to  their  right  to  satisfy  Rule  i,  and  also  to  the 
right  of  the  line  from  C. 

Illustration  7,  Fig.  3:  When  the  point  sought  is  on  the  circle  passing  through  the 
three  fixed  points,  the  position  is  indeterminate,  as  the  three  lines  will  intersect  at  one 
point,  although  the  table  is  imperfectly  oriented.  Another  selection  of  points  must  be 
made. 

Illustration  7,  Fig.  3:  When  the  point  sought  falls  within  one  of  the  segments  of  the 
great  circle,  the  line  drawn  from  A,  the  middle  point  is  to  the  right  of  the  intersection 
of  the  lines  from  B  and  C;  therefore  (Rule  3)  the  point  sought  must  be  on  its  right 
side,  and  also  (Rule  i)  to  the  right  of  the  line  from  B  and  from  C.  Locate  it  exactly 
according  to  Rule  i . 

Illustration  7,  Fig.  4:  When  the  point  sought  is  on  or  near  the  range  line  between 
the  fixed  points,  the  point  sought  must  be  between  the  parallel  lines  to  satisfy  the 
conditions  of  Rule  i .  Its  position  with  reference  to  the  intersecting  line  follows  from 
the  same  rule.  In  the  figure  the  point  sought  being  between  the  lines  from  B  and  C,  is 
to  the  right  of  each,  therefore  it  is  to  the  right  of  the  line  from  A. 

Illustration  7,  Fig.  5:  When  the  point  sought  falls  within  the  great  triangle,  it 
must  fall  within  the  triangle  of  error.  No  other  position  would  satisfy  the  conditions 
of  Rule  i. 

Illustration  7,  Fig.  6:  When  the  three  fixed  points  are  in  a  straight  line.  In  this 
case  the  points  are  considered  as  being  in  the  circumference  of  a  circle  of  infinite  diam- 
eter and  the  point  sought  always  lying  in  one  of  the  segments  of  the  great  circle.  The 
treatment  of  this  case  is  then  identical  with  that  of  Illustration  7,  Fig.  3. 

The  preceding  cases  are  all  examples  of  the  conditions  which  may  occur  when  the 
table  is  deflected  to  the  right.  By  turning  the  printed  side  of  the  illustration  to  the 
light  and  looking  at  the  figures  through  the  paper,  they  will  appear  reversed,  and  they 
will  then  be  examples  of  conditions  which  may  occur  when  the  table  is  deflected  to  the 
left. 

Repetition. — When  the  true  point  has  been  estimated  and  marked  on  the  sheet  in 
accordance  with  the  foregoing  rules,  a  new  orientation  is  made.  If  the  lines  from  the 
three  stations  now  intersect  at  that  point,  it  proves  the  estimate  to  have  been  correct 


NO.  8. 


Fig.  6 


Fig.  3 


THREE-POINT  AND  TWO-POINT  PROBLEMS. 


\ 


1       I 

1        • 

>    I 

'--£ 

e 

Fig.l 


p-**" 

Fig.  2 


Fig.  3 


d 
Fig.  4 


BESSEL'S  SOLUTION  OF  THREE-POINT  PROBLEM. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  313 

and  the  position  is  determined.  If  a  new  triangle  of  error  is  formed,  it  indicates  an 
erroneous  estimate,  and  the  operation  must  be  repeated. 

Orienting  by  estimation. — A  small  triangle  of  error  is  the  result  of  a  close  orienta- 
tion, which  the  topographer  endeavors  to  accomplish  at  the  first  trial  by  taking  advan- 
tage of  any  range  that  may  exist  either  of  signals  or  other  details  already  plotted  on 
the  sheet.  It  will  serve  the  same  purpose  if  they  are  near  enough  in  line  to  estimate  a 
direction  on  the  sheet  to  the  farthest  object,  and  then  to  orient  by  it. 

The  declinatoire  may  be  used,  but  it  is  a  slow  and  inaccurate  method  of  orientation. 

It  is  employed  for  this  purpose  by  placing  the  straight  edge  of  the  box  containing 
the  needle  upon  a  magnetic  meridian,  previously  traced  upon  the  map,  and  revolving 
the  table  until  the  needle  points  to  o°,  or  north,  on  the  graduated  arc  at  the  end  of  the 
box.  The  magnetic  meridian  is  roughly  determined  at  any  well-determined  station, 
when  the  table  is  properly  oriented  by  the  use  of  the  declinatoire  itself,  the  meridian 
line  being  drawn  upon  the  sheet  along  the  straight  edge  of  the  box  when  the  needle 
points  to  o°.  Or  the  table  may  be  oriented  by  making  the  straight  edge  of  the  box 
coincide  with  one  of  the  meridians  of  the  projection  and  then  turning  the  board  until 
the  needle  points  to  the  right  or  left  of  the  zero,  according  to  the  amount  and  direction 
of  the  magnetic  deviation. 

BesseVs  method  by  inscribed  quadrilateral  is  the  simplest  method  by  construction. 
The  objection  to  it  arises  from  the  fact  that  in  practice  the  intersection  of  the  construc- 
tion lines  often  falls  beyond  the  limit  of  the  board. 

By  this  method  a  quadrilateral  is  constructed  with  all  the  angles  in  the  circumfer- 
ence of  a  circle,  one  diagonal  of  which  passes  through  the  middle  one  of  the  three  fixed 
points  and  the  point  sought.  On  this  line  the  alidade  is  set,  the  telescope  directed  to 
the  middle  point,  and  the  table  is  in  position.  Resection  upon  the  extreme  points  inter- 
sects in  this  line  and  determines  the  position  of  the  point  sought. 

Illustration  9,  Figs,  i,  2,  3,  and  4.  L,et  a  b  c  be  the  points  on  the  sheet  represent- 
ing the  signals  A  B  C  on  the  ground.  The  table  is  set  up  at  the  point  to  be  determined 
(</),  and  leveled.  The  alidade  is  set  upon  the  line  ca,  and  a  directed,  by  revolving  the 
table  to  its  corresponding  signal  A,  and  the  table  clamped;  then,  with  the  alidade 
centering  on  c ,  the  middle  signal  B  is  sighted  with  the  telescope  and  the  line  ce  drawn 
along  the  edge  of  the  rule.  The  alidade  is  then  set  upon  the  line  ac  and  the  telescope 
directed  to  the  signal  C,  by  revolving  the  table,  and  the  table  clamped.  Then,  with 
the  alidade  centering  on  a,  the  telescope  is  directed  to  the  middle  signal,  B,  and  the  line 
ae  is  drawn  along  the  edge  of  the  rule.  The  point  e  (the  intersection  of  these  two  lines) 
will  be  in  the  line  passing  through  the  middle  point  and  the  point  sought.  Set  the 
alidade  upon  the  line  de,  direct  b  to  the  signal  B  by  revolving  the  table,  and  the  table 
will  be  in  position.  Clamp  the  table,  center  the  alidade  upon  a,  direct  the  telescope  to 
the  signal  A,  and  draw  along  the  rule  the  line  ad.  This  will  intersect  the  line  be  at  the 
point  sought.  Resection  upon  C,  centering  the  alidade  on  c  in  the  same  manner  as 
upon  A,  will  verify  its  position. 

The  opposite  angles  of  the  quadrilateral  adce  being  supplementary, 

£ace  and  /.ade  are  subtended  by  the  same  chord  ae,  and  Z.cae  and  Z.cde  are  sub- 
tended by  the  same  chord  ce;  consequently,  the  intersection  of  ae  and  ce  at  e  must  fall 
on  the  line  db;  or,  the  segments  of  two  intersecting  chords  in  a  circle  being  reciprocally 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

proportional,  the  triangles  adf  and  cef  are  similar,  and  the  triangles  cdf  and  aef  are 
similar,  and  d,  /,  and  e  must  be  in  a  right  line  passing  through  b. 

In  using  this  method  the  triangle  formed  by  the  three  fixed  points  can  be  contracted 
or  extended,  as  may  be  desirable,  by  drawing  a  line  parallel  to  the  one  joining  the  two 
extreme  points,  and  terminated  by  those  joining  the  extremes  with  the  middle  point. 
The  graphic  solution  can  then  proceed  in  the  same  manner  as  that  described  for  an  orig- 
inal triangle. 

Tracing-cloth  protractor. — The  third  method  consists  in  laying  off  the  angles  between 
the  three  known  points  on  tracing  cloth  or  paper,  and  using  this  as  a  protractor,  deter- 
mine the  position  of  the  unknown  point. 

Fasten  a  sheet  of  tracing  cloth  or  paper  to  the  board,  marking  upon  it  a  point  to 
represent  the  unknown  point.  Draw  through  it  lines  toward  the  three  known  points. 
Then  shift  the  tracing  cloth  over  the  sheet  until  each  of  the  three  lines  passes  through 
the  plotted  point  corresponding  to  the  point  toward  which  it  is  drawn.  The  position  of 
the  unknown  point  will  be  at  the  intersection  of  these  lines. 

This  method  is  less  exact  and  not  so  convenient  as  the  other  two  previously  described, 
and  is  impracticable  when  the  wind  blows. 

TWO-POINT  PROBLEM. 

The  occasion  may  arise  where  it  is  desirable  to  place  the  table  in  position  at  a  given 
point,  from  which  only  two  determined  points  are  visible.  This  may  be  done  by  the 
following  methods: 

One  method  possesses  the  virtue  of  requiring  no  linear  measurements,  and  demon- 
strates in  a  very  satisfactory  manner  the  effectiveness  of  the  table  in  determining  posi- 
tion by  resection. 

(Illustration  8,  Figs.  2,3,4  and  5- ) :  Two  points,  A  and  B,  not  conveniently  access- 
ible, being  given,  by  their  projections  a  and  b,  to  put  the  plane  table  in  position  at  a  third 
point,  C.  (The  capital  letters  refer  to  points  on  the  ground,  and  the  small  ones  to  their 
corresponding  proj  ections . ) 

Select  a  fourth  point,  D,  so  that  the  intersections  from  C  and  D  upon  A  and  B 
make  sufficiently  large  angles  for  good  determinations.  Put  the  table  approximately  in 
position  at  D,  by  estimation  or  by  compass,  and  draw  the  lines  Aa  and  B£,  intersecting 
at  d;  through  d  draw  a  line  directed  to  C.  Then  set  up  at  C,  and  assuming  the  point  c  on 
the  line  dC,  at  an  estimated  distance  from  d,  and  putting  the  table  in  a  position  parallel 
to  that  which  is  occupied  at  D,  by  means  of  the  line  cd,  draw  the  lines  from  c  to  A  and 
from  c  to  B.  These  will  intersect  the  lines  dA  and  dB  at  points  a'  and  b' ,  which  form 
with  c  and  d  a  quadrilateral  similar  to  the  true  one,  but  erroneous  in  size  and  position. 

The  angles  which  the  lines  ab  and  a'b'  make  with  each  other  is  the  error  in  posi- 
tion. By  drawing  through  c  a  line  cd'  making  the  same  angle  with  cd  as  that  which  ab 
makes  with  a'b' ,  and  directing  this  line  cd'  to  D,  the  table  will  be  brought  into  position, 
and  the  true  point  c  can  be  found  by  the  intersections  of  a  A  and  £B. 

Instead  of  transferring  the  angle  of  error  by  construction,  we  may  conveniently  pro- 
ceed as  follows,  observing  that  the  angle  which  the  line  a'b'  makes  with  ab  is  the  error 
in  the  position  of  the  table.  As  the  table  now  stands,  a'b'  is  parallel  with  AB,  but  we 
want  to  turn  it  so  that  ab  shall  be  parallel  to  the  same  line.  Place  the  alidade  on  a'V 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  315 

and  set  up  a  mark  in  that  direction,  then  place  the  alidade  on  ab  and  turn  the  table 
until  it  again  points  to  the  mark,  then  ab  will  be  parallel  to  AB,  and  the  table  is  in 
position. 

Another  method  is  as  follows  (Illustration  8,  Fig.  6): 

Two  points,  A  and  B,  not  conveniently  accessible,  being  given  by  their  projections 
a  and  b,  to  put  the  plane-table  in  position  at  a  third  (undetermined)  point,  C. 

Set  up  the  table  at  the  point  sought  as  closely  oriented  as  can  be  done  by  estimation, 
and  resect  upon  A  and  B,  intersecting  the  line  be  at  c' .  The  angle  ac'b  is  the  true 
angle  at  the  point  occupied,  subtended  by  AB,  being  the  angle  of  nature  actually  drawn; 
therefore,  the  true  point  must  be  on  the  circumference  of  the  circle  passing  through  abc1 . 
Construct  this  circle.  Measure  off  a  base,  CD,  at  least  half  the  length  of  CB,  at  right 
angles,  or  nearly  so,  to  be,  in  either  direction  most  convenient.  Set  up  a  signal  at  D, 
and  with  the  alidade  draw  the  line  c'd.  Remove  the  table  to  D,  and,  by  means  of  a 
signal  at  C  (the  point  sought),  and  the  line  dc' ,  bring  the  table  into  a  position  parallel 
to  that  which  it  occupied  at  C.  With  the  alidade  centering  on  d,  observe  the  signal  B, 
and  draw  the  line  db1  intersecting  cb  at  b' .  c'b1  is  the  distance  of  the  point  C  from  B, 
and  this  distance  laid  off  on  the  circle  ac'b  as  a  chord  from  b  will  give  c" ',  the  true  posi- 
tion of  the  point  C.  A  fourth  point  may  then  be  occupied,  and  by  resection  upon  A, 
B,  and  C  the  accuracy  of  the  determination  of  C  verified. 

Where  it  is  possible  to  get  the  two  signals  A  and  B  in  range,  it  is  easy  to  determine 
the  position  of  a  third  point  by  a  method  long  practiced  by  topographers. 

Set  up  the  table  anywhere  on  the  range  line,  and  orient  by  the  latter.  Resect  on 
the  unknown  point,  drawing  the  line  anywhere  on  the  sheet  most  convenient.  L/eave  a 
signal  at  the  occupied  point  on  the  range  line  and  set  up  the  instrument  at  the  unknown 
point.  Orient  by  the  line  drawn  when  at  the  station  on  the  range  line,  sighting  on  the 
latter  station.  The  table  will  now  be  in  a  parallel  position  to  that  when  on  the  range 
line,  which  is  the  true  position,  and  the  unknown  point  may  be  determined  by  resec- 
tion upon  the  two  fixed  points  and  their  projections. 

Deflection  of  long  lines. — In  adjusting  lines  of  intersection  upon  a  point  or  object 
from  a  series  of  stations,  when  these  lines  do  not  coincide  in  one  point,  as  they  are 
usually  derived  from  signals  at  unequal  distances,  the  error  should  not  be  divided  equally 
among  them,  but  in  proportion  to  their  lengths  if  the  discrepancies  are  not  eliminated 
by  the  rules  for  distortion  errors  given  later. 

It  should  be  borne  in  mind  that  very  short  lines  from  a  determined  point — as,  for 
instance,  to  the  corners  of  a  fenced  road,  where  the  table  occupies  the  center  of  the 
intersection  of  two  roads — may  be  taken  with  no  apparent  error  when  the  table  is 
deflected  to  some  extent  from  its  true  azimuth,  but  that  in  this  case  a  prolonged  line 
will  be  considerably  out  at  its  further  extremity. 

A  long  line  should  never  be  obtained  by  the  prolongation  of  a  short  one  from  a  back 
station  where  there  is  no  small  check  line,  or  some  other  point  in  that  prolongation 
already  fixed. 

It  will  be  apparent  that  the  more  nearly  at  right  angles  intersecting  lines  cross  each 
other  the  more  clearly  the  point  will  be  defined;  acute  intersections,  as  far  as  possible, 
should  be  avoided,  and,  even  when  they  are  crossed  by  a  third  line  at  a  satisfactory 
angle,  a  fourth  line,  or  an  accurate  rod  reading  from  a  well-determined  point,  is  advis- 
able if  within  reach. 


316 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Sometimes  a  position  is  established  by  measuring  along  the  estimated  direction 
from  a  near-by  fixed  point  and  then  orienting  by  this  assumed  position  and  a  distant 
point.  This  method  should  be  used  with  caution,  but  is  generally  reliable  for  rodding 
the  detail  in  the  vicinity. 

Distortion  errors* — The  distortion  of  a  plane-table  sheet  destroys  the  perfect  propor- 
tions which  exist  between  the  fixed  points  and  their  plotted  representatives  on  the  sheet. 

The  diagram  illustrates  the  effect  distortion  would  have  in  the  determination  of  a 
point. 

NO.  10. 


A,  B,  C,  etc.,  are  plotted  in  their  true  relations.  After  the  sheet  has  contracted, 
a,  6,  c,  etc.,  represent  the  relations  those  points  have  assumed.  The  paper  contracts 
at  a  uniform  but  different  rate  in  each  direction. 

The  plane-table  is  supposed  to  be  at  X,  the  exact  center  of  the  figure,  and  it  is 
required  to  determine  the  position  by  the  distorted  points  a,  b,  c,  etc.  By  reversing  the 
telescope,  we  immediately  ascertain  that  we  are  directly  on  the  line  HD.  Reversal 
will  also  show  that  we  are  on  the  lines  AE,  CG,  and  BF.  But  the  distortion  is  not 
apparent  until  the  telescope  is  pointed  at  the  signals,  and  the  lines  are  drawn  on  the 
sheet.  Then  if  we  orient  by  the  line  HD,  we  shall  produce  the  figure  of  the  diagram, 
giving  five  determinations,  i,  2,  3,  4,  and  X,  each  made  with  four  well-conditioned 
points.  Any  one  of  these  conditions  would  be  considered  satisfactory  if  we  had  not  the 
other  points  to  show  that  something  was  wrong.  To  orient  by  the  line  BF  will  produce 
the  same  result.  But  if  we  take  the  diagonal  AE,  we  shall  have  two  positions  at  5  and 
7,  formed  by  the  intersection  of  the  diagonal  points,  with  the  lines  from  the  other  points 


*See  Distortion  of  Plane  Table  Sheets,  Ogden,  Science,  Vol.  XI,  No.  270. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  317 

running  wild.  Using  the  diagonal  CG  would  give  two  points  at  6  and  8,  with  the  lines 
from  the  other  points  running  wild  as  before. 

Position  by  compromise. — There  is  no  question  that  out  of  the  nine  positions  devel- 
oped by  these  settings,  that  at  X  is  the  only  true  compromise.  When  the  sheet  is  dis- 
torted, all  positions  are  compromises;  and  X  is  the  true  compromise  in  this  case,  for  it 
is  on  the  lines  CG,  AE,  etc. :  a  below  and  e  above,  the  line  connecting  A  and  £t  by 
equal  quantities.  A  line  drawn  through  the  distorted  points  a  and  e  must  pass  through 
the  middle  point  X.  The  positions  5,  6,  7,  and  8  can  not  be  true,  because  lines  forming 
them  will  not  pass  through  the  opposite  points  when  extended,  which  we  know  to  be 
the  condition  that  must  be  filled. 

Rules: 

(1)  A  station  made  with  three  points  that  are  on  the  lines  of  contraction,  the 
resecting  lines  forming  nearly  right  angles  at  their  intersection,  will  give  the  true  posi- 
tion in  relation  to  all  points  in  the  sheet  (as  h,  b,  d~). 

(2)  A  similar  condition  of  right-angular  intersection  at  the  station,  but  the  lines 
forming  diagonals  to  the  lines  of  contraction,  will  give  the  worst  possible  position  for 
the  station  (as  a,  c,  and  e). 

(3)  A  station  made  with  three  points  on  one  of  the  lines  of  contraction  will  give 
the  correct  orientation  of  the  table  (a,  h,  and  c)  but  not  the  correct  position. 

(4)  In  estimating  errors  of  the  point  due  to  distortion,  those  situated  on  the  lines 
of  contraction  require  no  allowance,  however  distant. 

Application. — If  the  change  in  the  sheet  due  to  contraction  or  expansion  gives  the 
same  percentage  of  the  units  of  length,  both  lengthwise  and  transverse  of  the  sheet,  the 
points  are  still  in  their  true  relative  position,  and  the  projection  is  practically  as  good 
as  when  laid  on  the  paper,  but  is  on  a  slightly  altered  scale.  When  the  percentage 
of  change  in  the  units  of  length  is  greater  in  one  direction  than  the  other,  the  sheet  and 
projection  are  distorted;  and  to  make  a  station  by  the  three-point  problem,  the  change 
of  scale  in  each  direction  must  be  allowed  for.  The  difficulty  in  making  such  allow- 
ances is  not  great,  if  the  principal  effects  of  distortion  in  the  sheet  are  borne  in  mind.  It 
would  not  be  permissible,  even  were  it  practicable,  to  make  new  points  on  the  sheet,  as 
this  would  destroy  the  geographic  position.  It  is  necessary,  therefore,  to  assume  the 
new  points  by  estimation,  applying  the  percentage  of  change  to  the  distances  measured 
between  the  points  on  the  lines  of  change — that  is,  on  lines  parallel  to  the  edges  of  the 
sheet.  If  the  point  occupied  and  the  point  sighted  to  are  on  a  line  parallel,  or  nearly 
so,  to  one  edge  of  the  sheet,  its  movement  from  the  distortion  can  only  be  along  that 
line.  When  the  position  of  the  point  sighted  to  is  found  situated  to  one  side  of  the  line 
parallel  to  the  edge  of  the  sheet,  the  distortion  will  also  affect  it  in  the  direction  at  right 
angles  to  that  edge,  and  the  effect  of  the  distortion  will  be  most  apparent  when  the 
angle  of  deflection  is  45°  and  the  position  at  as  great  a  distance  from  the  point  occupied 
as  the  paper  will  permit.  As  the  angle  of  deflection  increases  above  45°  the  effect 
becomes  less  and  disappears  at  90°,  when  the  position  will  fall  again  in  a  line  parallel 
to  an  edge  of  the  sheet. 

Referring  to  the  diagram,  Illustration  10,  to  make  a  station  with  the  three  points  a, 
b,  c:  If  the  sheet  were  not  distorted,  the  station  would  be  at  X;  A,  B,  and  C  being  the  true 
positions  plotted  when  the  projection  was  drawn.  But  the  sheet  having  contracted,  a, 
b,  and  c  show  the  relative  positions  of  these  points;  therefore  we  make  such  allowance 


-7Zg  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

for  the  contraction  derived  from  measuring  the  unit  of  length  that  we  can  place  or 
imagine  a  and  c  to  be  where  the)'  belong,  at  A  and  C.  b  requires  no  change,  as  it  is  on 
a  line  parallel  to  the  edge  of  the  sheet.  To  locate  A  we  must  know  the  distances 
(approximately)  h  to  a  and  h  to  X,  which,  multiplied  by  the  percentages  of  contraction 
(in  this  case),  will  give  the  distance  of  A  above  and  to  the  left  of  a.  The  same  process 
locates  C. 

If  the  station  were  to  be  made  with  the  points  a,  c,  and  e,  all  three  points  would 
have  to  be  imagined  in  a  new  position  by  the  same  process  that  A  has  been  located. 

Stations  made  in  this  way  will  be  good  for  all  local  sketching  within  an  area  that 
the  contraction  of  the  sheet  is  inappreciable;  but  to  take  cuts  on  distant  objects  from 
such  a  station  the  orientation  of  the  table  must  be  changed.  If  an  object  is  somewhere 
near  the  direction  of  a  and  the  table  at  the  compromise  station  X,  the  table  must  be 
oriented  by  a  and  X,  the  imaginary  position  A  being  discarded. 

The  same  processes  apply  to  all  positions  on  the  sheet  for  the  station  occupied. 

Height  of  instrument. — Having  obtained  the  horizontal  position  on  the  sheet  of  the 
occupied  point,  the  next  proceeding  in  the  logical  sequence  is  the  determination  of  the 
height  of  the  instrument  above  some  datum  plane,  in  order  to  locate  and  draw  the  con- 
tours of  the  area  surrounding  the  station.  The  angle  read  and  the  distance  between 
the  occupied  point  and  the  observed  point  measured  from  the  map,  the  height  is  com- 
puted by  means  of  the  tables  to  be  found  at  the  end  of  the  Manual,  or  the  result  can 
be  obtained  mechanically  by  using  the  hypsograph. 

This  instrument  was  designed  by  Assistant  Fremont  Morse  for  use  in  the  Coast 
and  Geodetic  Survey  and  differs  from  the  ordinary  form  of  topographic  slide-rule  used 
by  engineers  in  three  particulars:  First,  it  is  circular  instead  of  rectilinear;  second,  it 
does  not  give  elevations  in  the  same  unit  as  the  distances,  but  gives  heights  in  feet 
when  the  distances  are  measured  in  meters;  and  third,  the  arguments  used  for  deter- 
mining the  heights  are  the  horizontal  distance  and  angle  of  elevation  instead  of  inclined 
distance  and  angle  of  elevation. 

The  instrument  will  indicate  the  difference  of  height  (uncorrected  for  curvature 
and  refraction)  for  any  distances  and  angles  encountered  in  ordinary  topographic  work, 
with  an  error  much  smaller  than  the  probable  error  of  observation  of  the  plane-table 
alidade. 

For  complete  description  and  directions  for  use,  see  Appendix  4,  Report  for  1902. 

Relief. — There  are  two  methods  of  representing  it — by  hill  shading  and  by  contours. 

Hill  shading  is  generally  effected  by  a  system  of  lines,  called  hachures,  drawn  in 
the  direction  of  the  slope.  When  it  is  steep,  the  hachures  are  thick  and  closely  spaced. 
On  the  other  hand,  a  gentle  incline  will  be  indicated  by  fine  lines  widely  separated. 

Contours  *  or  horizontal  curves  are  the  outlines  of  horizonal  sections  of  ground  at 
different  elevations  with  designated  equal  intervals  between  their  planes,  delineated  in 
their  true  positions  relatively  to  each  other  and  to  the  rest  of  the  map,  and  conforming 
to  the  scale  of  the  map  itself;  or,  briefly,  a  contour  is  a  curve  produced  by  the  intersec' 
tion  of  the  horizontal  plane  with  the  surface  of  the  ground.  They  may  also  be  described 

*For  interesting  articles  on  the  diagrammatic  properties  of  the  contour  line  see:  On  Contour  and 
Slope  Lines,  Cayley,  I/ondon  &  Ed.  Mag.,  1859,  pp.  264-268;  On  Hills  and  Dales,  Clerk  Maxwell, 
ibid,  1870,  pp.  421-426;  Properties  of  Matter,  Tait,  1890,  pp.  70-81. 


NO.   11. 


HYPSOQRAPH. 


NO.  12. 


SIDE  VIEW 


TOP  VIEW 


SECTION 


HYSOQRAPH. 


Diagram.  iULustrattna  the  mode  of  constructing  Profile  from.  Plan, 


No.  14 


ejrf,  Jface,  and  ToZiw  o/a  Granite  Cliff  (Eagle  Cliff,  Mt.Deiti'ri  Id.) 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  319 

as  imaginary  shore  lines  formed  at  stated  or  regular  elevations,  by  water  which  is  sup- 
posed to  rise  successively  to  these  elevations  over  the  face  of  the  country. 

Profile. — As  each  curve  has  equal  vertical  ordinates  at  all  points,  the  elevation  or 
profile  of  a  hill,  as  well  as  a  model  in  relief,  can  be  constructed  from  the  map,  when  it 
is  accurately  executed  on  a  large  scale,  without  further  field  measurements. 

A  profile  of  a  hill  is  the  outline  or  trace  formed  with  its  surface  by  a  vertical  plane 
cutting  the  hill  in  any  direction. 

Illustration  No.  13  shows  the  profile  through  the  line  A'  B'  of  the  hill  h,  as  repre- 
sented on  a  topographic  map.  The  full  parallel  lines  upon  the  profile  represent  the 
successive  heights  or  sections  of  the  hill  of  20  feet,  and  the  broken  or  intermediate  lines 
xxx  those  of  10  feet.  A  reference  to  the  letters  of  the  diagram  is  all  that  is 
necessary  to  a  full  understanding  of  the  subject:  a  is  the  shore  line  or  high- water  line 
upon  the  map,  xxx  are  the  auxiliary  lo-foot  curves;  f  the  coincidence  of  curves 
upon  the  chart  at  the  perpendicular  face  of  the  hill  /,  upon  the  section.  This  is  the 
only  case  where  contours  of  different  heights  run  into  each  other  upon  a  topographic 
plan,  n  is  a  depression  in  the  face  of  the  hill,  represented  on  the  profile  by  D.  d'  is 
a  barranca  or  dry  broken  gully,  and  c'  c'  a  water  course. 

It  will  be  plain  that  if  we  were  to  suppose  the  water  to  rise  to  a  height  of  20  feet 
above  the  high-water  line,  to  h  on  the  profile,  the  2o-foot  curve  upon  the  map  would 
become  the  shore  line  and  the  depression  D'  would  fill  up  and  become  a  pond  of  water; 
and  if  the  water  were  to  rise  to  a  height  of  30  feet,  the  dotted  broken  line  would  form 
a  shore  line,  and  the  knoll  G  would  become  an  island. 

Advantages  and  disadvantages  of  hill  shading  and  contours. — In  a  mountainous 
country  the  method  of  hill  shading  presents  a  picture  which  expresses  more  forcibly  to 
the  eye  the  configuration  of  the  country  than  a  system  of  contours.  But  the  objection 
to  its  sole  use  arises  from  the  fact  that,  although  one  ridge  is  perceived  to  be  higher 
than  another,  there  is  no  guide  for  stating  in  terms  of  some  linear  unit  this  difference 
in  elevation.  It  also  obscures  the  symbols  representing  other  details  on  the  surface. 

A  system  of  contours  furnishes  a  convenient  means  for  obtaining  the  heights  on 
any  part  of  a  map,  but  does  not  adapt  itself  to  the  representation  of  the  small  but 
important  accidents  of  the  ground,  such  as  gullies,  ledges,  rocks,  etc.;  nor  does  it 
satisfactorily  delineate  such  features  as  cliffs,  bluffs,  quarries,  railroad  cuts,  and 
embankments. 

For  these  reasons  the  Coast  and  Geodetic  Survey  has  adopted  both  methods, 
employing  hachures  for  the  smaller  features  and  where  the  steepness  of  the  slope  would 
make  the  contour  lines  approach  together  so  closely  that  individual  lines  would  become 
indistinguishable,  and  relying  on  the  contours  to  delineate  less  precipitous  ground. 

The  two  systems  can  be  seen  combined  when  it  is  necessary  to  indicate  a  rocky  and 
broken  mountain  face.  (Illustrations  14  and  15.) 

The  contour  interval  customarily  used  on  the  Coast  and  Geodetic  Survey  field  sheets 
is  20  feet.  When,  however,  the  contour  runs  very  near  to  some  remarkable  accident 
of  ground,  as  a  prominent  spur  or  indentation,  a  slight  deviation  above  or  below  its  true 
plane  is  admissible  to  include  this  feature,  although  it  is  preferable  to  avoid  doing  so,  if 
possible,  by  the  introduction  of  an  auxiliary  curve. 

In  abruptly  mountainous  and  comparatively  inaccessible  regions,  where  sketching 
must  be  relied  upon,  ico-foot  curves  may  suffice  to  develop  all  necessary  features. 

75930°— 15 3 


320 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Datum  plane. — Probably  the  best  plane  of  reference  for  heights  of  points  on  the 
earth's  surface  is  the  mean  level  of  the  sea,  since  the  mean  of  the  rise  and  fall  of  the 
tides  is  approximately  this  level.  In  practice,  however,  mean  high  water  is  usually 
taken,  as  it  includes  all  land  not  covered  by  the  tide  range,  and  is  the  line  dividing 
land  and  water. 

Reference  signal. — It  is  advisable  in  commencing  the  survey  of  a  region  bordering 
on  tide  water  to  locate  one  or  more  signals  at  the  assumed  high- water  line,  carefully 
noting  the  height  of  the  top  of  the  flag  above  the  same,  to  be  used  in  measuring  angles 
of  depression  for  heights  from  points  occupied  during  the  progress  of  the  graphic  trian- 
gulation.  As  the  heights  of  other  points  are  determined  in  the  course  of  the  survey  and 
verified  from  observations  from  two  or  three  other  points,  these  in  turn  may  be  used  for 
the  same  purpose. 

The  following  are  the  methods  of  surveying  curves  of  equal  elevation : 

First.  The  determination  of  the  position  and  heights  of  a  number  of  characteristic 
points  of  the  terrene,  and  with  these  as  guides  tracing  the  contour  lines. 

This  is  the  method  generally  used  in  surveys  embracing  such  areas  as  the  sheets  of 
the  Coast  and  Geodetic  Survey  on  scales  of  i-ioooo  and  1-20000. 

It  has  the  merit  that  the  development  of  the  terrene  proceeds  with  the  survey  of 
the  skeleton,  and  does  not  necessitate  a  return  to  a  station  when  once  occupied.  In 
connection  with  the  determination  of  position  by  resection  it  works  harmoniously  and 
economically,  since  points  that  would  be  selected  for  position  as  having  the  best  outlook 
are  likely  to  be  the  characteristic  ones  of  the  terrene. 

Second.  Surveying  and  leveling  the  skeleton  and  its  traverses. 

Third.  Surveying  and  leveling  the  profile  lines. 

The  profile  is  a  traverse  line  on  which  are  determined  the  heights  of  the  points  at 
which  the  surface  changes  slope.  The  points  where  this  line  is  intersected  by  the  suc- 
cessive contour  interval  are  easily  determinable  with  the  level  and  rod. 

Fourth.  Surveying  and  leveling  the  base  of  each  level  section. 

To  determine  the  base  of  each  level  section  the  table  is  set  up  in  position  where  this 
level  intersects  the  profile,  and  using  the  alidade  as  a  leveling  instrument,  with  a  target 
fixed  on  the  rod  at  the  height  of  the  optical  axis  of  the  telescope,  the  line  is  traced  by 
locating  the  rod  in  successive  positions  at  characteristic  points  of  the  terrene,  when  the 
target  comes  in  the  horizontal  plane  of  the  optical  axis,  direction  and  distance  of  the 
rod  being  determined  and  drawn  in  each  case.  A  line  drawn  through  these  points, 
recognizing  features  between  the  stations,  locates  the  curve.  In  this  operation  allow- 
ance should  be  made  for  curvature  and  refraction,  when  the  distance  becomes  sufficiently 
great  to  make  it  a  factor. 

Fifth.  Surveying  and  leveling  the  parts  of  several  level  sections  from  one  station. 

When  parts  of  several  level  sections  are  run  from  one  station,  set  up  the  table  at  a 
point  on  a  contour,  and  observe  on  a  staff  the  height  of  the  optical  axis  of  the  alidade. 
Set  a  target  on  the  staff  above  this  height  as  many  contour  intervals  as  its  length  will 
include.  The  aid  carries  the  staff  below  the  instrument  and  is  signaled  to  stop  when 
the  target  comes  in  the  horizontal  plane  of  the  optical  axis,  and  at  successive  steps 
traverses  the  lower  curve.  The  target  is  then  lowered  on  the  staff  one  contour  interval 
and  the  next  curve  above  is  traced  in  the  same  manner,  continuing  the  proceeding  until 
the  level  of  the  instrument  is  reached,  when  the  table  is  moved  to  an  upper  station 


NO.   16. 


Fig.l 


Fig.  2 


Kg.  3 


Fig.  5 


Fig.  6 


Fig.  8 


TYPICAL  CONTOUR  GROUPS. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  321 

and  the  proceeding  continued  until  the  summit  is  reached.  (Applies  only  to  very  small 
contour  intervals. ) 

Sixth.   The  division  of  the  terrene  into  squares,  triangles,  or  parallelograms. 

By  the  mode  of  regular  division  of  the  surface  into  squares,  triangles,  or  parallelo- 
grams, pegs  are  driven  at  regular  intervals,  and  their  heights  determined  by  level  in  the 
way  that  may  be  most  convenient,  a  spirit-leveling  instrument  being  the  most  accurate. 

Station  routine. — The  topographer  having  determined  his  position  on  the  sheet, 
and  also  the  height  of  the  instrument,  proceeds  to  map  the  natural  and  artificial  details 
of  the  area  surrounding  the  station.  For  this  purpose  the  direction  of  each  detail  is 
obtained  by  pointing  the  telescope  upon  it,  the  edge  of  the  rule  cutting  the  station 
point;  its  distance  is  determined  by  reading  the  stadia  rod  held  there  for  the  purpose. 
This  distance  is  then  taken  off  the  metal  scale  with  a  pair  of  dividers  and  plotted 
along  the  edge  of  the  rule. 

While  this  is  in  progress  the  alidade  is  used  both  as  a  level  for  the  observation  of 
objects  of  the  same  height  as  the  instrument  and  for  measuring  angles  of  elevation  and 
depression  to  such  of  the  plotted  details  whose  position  at  critical  points  of  the  contours 
would  materially  assist  the  topographer  in  tracing  them. 

Number  of  elevations  to  be  determined. — No  rule  can  be  laid  down  as  to  the  number 
of  elevations  that  should  be  determined  from  each  plane-table  station  or  for  a  given 
area.  It  will  depend  on  the  skill  of  the  topographer  and  the  modeling  of  the  ground. 
The  number  will  be  adequate  when  he  is  confident  of  tracing,  by  their  aid,  the  contours 
with  an  accuracy  sufficient  for  the  scale  and  the  purpose  of  the  survey. 

It  would  indicate  careless  and  slovenly  work  if  the  contours  were  found  on  exam- 
ination to  deviate  frequently  from  their  true  position  on  the  sheet  by  more  than  half  an 
interval  for  a  slope  of  less  than  5°  in  an  open  country.  When  the  slope  is  steeper,  or 
in  wooded  regions,  a  greater  latitude  is  permissible,  but  even  here,  in  representing  the 
crests  of  ridges,  prominent  hill  tops,  and  valley  floors,  this  limit  of  half  an  interval  should 
not  be  departed  from  for  good  work.* 

Contour  sketching. — The  topographer  will  be  assisted  in  sketching  contours,  where 
the  modeling  is  intricate,  by  lightly  drawing  a  skeleton  composed  of  the  ridge  lines  and 
thalweg  lines  (lowest  lines  of  valleys)  in  their  proper  positions  around  the  station.  On 
the  ridge  lines  will  be  found  the  extreme  outward  or  convex  bends  of  the  contours,  and 
on  the  thalweg  lines  the  extreme  inward  or  concave  bends. 

It  can  be  readily  imagined  that  if  each  spur  and  each  small  depression  was  repre- 
sented by  its  appropriate  line,  and  on  each  of  them  were  located,  either  by  observation 
or  estimation,  points  having  elevations  equal  to  some  multiple  of  the  contour  interval, 
it  would  be  only  necessary  to  connect  those  points  having  the  same  elevation  with  a 
smooth  curve  to  have  a  correct  plan  of  the  contours. 

It  will  simplify  the  sketching  at  a  station  to  draw  the  highest,  lowest,  and  middle 
contours  first,  as  they  will  then  serve  as  guides  for  estimating  the  position  of  the  others. 

Typical  contour  groups  (Illustration  16). — It  should  be  remembered  that  a  con- 
tour never  splits,  as  shown  in  Fig.  i ;  nor  do  two  contours  run  into  one,  as  shown  in 


*  For  some  pertinent  remarks  on  this  subject  see  Bulletin  of  the  University  of  Wisconsin,  Eng. 
Series,  Vol.  i,  No.  10,  Topographical  Surveys;  their  methods  and  values.  J.  F.  Van  Ornum,  pp. 
360-361. 


322 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Fig.  2;  nor  cross  each  other,  except  in  the  rare  instance  of  an  overhanging  cliff,  as 
shown  in  Fig  3. 

When  an  auxiliary  contour  is  introduced,  no  more  of  it  is  drawn  than  is  sufficient 
to  delineate  the  special  feature  which  makes  it  necessary.  A  principal  contour,  on  the 
other  hand,  can  not  have  an  end  within  the  map;  if  it  commences  at  one  edge  it  must 
terminate  at  another. 

A  closed  contour  encircled  by  one  or  more  closed  contours  is  either  a  hill,  as  shown 
in  Fig.  5,  or  a  depression,  as  shown  in  Fig.  6;  the  arrows  showing  the  direction  in 
which  water  would  run.  The  summits  of  all  the  hills  of  importance  should  have  their 
elevations  determined  and  marked  on  the  map.  All  depressions  without  an  outlet  and 
which  do  not  contain  a  pond  or  lake  should  be  marked  with  a  D  at  their  lowest  point. 

A  series  of  contours,  as  shown  in  Fig  4,  is  either  a  croupe  (the  end  of  a  ridge  or 
promontory)  or  a  valley.  If  a  croupe,  the  contours  will  have  their  concave  sides 
toward  the  higher  ground;  if  a  valley,  the  contours  will  have  their  concave  sides  toward 
the  lower  ground. 

A  combination  of  four  sets,  like  Fig.  7,  with  convex  sides  turned  toward  each  other, 
represents  a  dip  in  a  ridge,  or  the  junction  of  two  ridges,  and  is  called  a  saddle. 

A  pass  in  a  mountain  range  generally  takes  the  form  shown  in  Fig.  8. 

Order  of  development  of  contours. — As  the  progress  of  topographic  work  is  usually 
from  the  shore  line  inward,  this  affords  the  most  favorable  direction  for  drawing  the 
curves  of  equal  elevation,  and  as  it  is  desirable  that  all  work  at  a  station  shall  be  com- 
pleted when  it  is  first  occupied  to  avoid  the  necessity  of  returning  to  it,  the  curves  should 
be  drawn  by  estimation  from  the  shore  line  to  the  points  sighted  and  determined  for 
position  and  height,  to  be  checked  by  drawing  from  those  points  when  in  turn  occupied. 
The  heights  of  a  sufficient  number  of  points  must  be  determined  to  guard  against  any 
wide  range  of  estimate  of  height  by  the  eye. 

In  abrupt  slopes  of  considerable  extent  the  use  of  a  pocket  clinometer  is  valuable 
in  determining  the  degree  of  slope,  and  in  order  to  draw  the  curves  by  the  widths  of 
their  zones  (the  cosines  of  angles  of  slope)  from  a  paper  scale  prepared  for  the  purpose. 
(See  Illustration  32.) 

Filling  in. — Having  completed  the  work  at  a  given  station,  the  topographer  proceeds 
with  his  party  and  instruments  to  an  adjoining  locality,  where  he  selects  a  new  station 
from  which  he  can  gather  the  details  of  an  area  bordering  upon  the  one  last  surveyed. 
In  this  manner  the  skeleton  map  is  filled  in  by  successively  occupying  stations  over  the 
whole  expanse  of  the  sheet. 

Traverse  lines. — In  a  wooded  country,  where  it  is  impossible  to  find  open  space  with 
range  sufficient  to  see  enough  points  for  determination  of  position  by  resection,  it  is 
necessary  to  run  traverses  along  the  roads,  with  offsets  to  such  lateral  features  as  it 
may  be  practicable  to  reach  without  the  expenditure  of  excessive  labor  and  time  in 
opening  lines  of  sight.  The  levels,  when  necessary,  are  carried  along  with  the  line  by 
observing  vertical  angles  with  the  alidade  upon  some  mark  on  the  rod,  taking  back  and 
fore  sights  at  alternate  stations. 

Main  traverse. — The  standard  table  is  used  on  main  roads  and  whenever  the  details 
are  important  and  numerous. 

The  traverse  line  is  started  by  occupying  some  point  previously  determined  and 
sending  the  telemeter  rod  ahead  to  a  place  selected  for  its  advantageous  position,  in 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  323 

reference  either  to  the  surrounding  features  or  facility  in  obtaining  a  new  section  of 
the  traverse. 

Having  sighted  to  this  point,  read  and  plotted  the  distance,  short  guide  lines  should 
be  drawn  along  the  edge  of  the  ruler  at  both  ends  and  numbered  or  lettered,  so  they 
may  be  identified  from  others  of  like  character.  The  table  is  then  moved  to  the  forward 
station,  approximately  oriented  by  estimation,  and  the  plotted  point  carefully  plumbed 
over  the  one  on  the  ground. 

The  alidade  is  now  placed  on  the  table,  and  the  table  oriented  by  bringing  the  edge 
of  the  ruler  close  up  to  the  guide  lines;  then  revolving  the  table  until  the  vertical  wire 
bisects  the  rod  or  signal  left  for  that  purpose  at  the  last  station. 

The  same  processes  which  were  employed  at  the  initial  station  are  now  repeated; 
the  detail  is  mapped  and  the  new  station  in  advance  occupied  in  turn,  the  line  progress- 
ing in  this  manner  by  successive  steps. 

In  running  traverses,  great  care  should  be  taken  to  sight  as  low  as  possible  upon 
the  fore  and  back  signals,  so  as  to  avoid  any  error  of  deflection  which  might  arise  from 
the  inclination  of  the  signal  poles. 

Subordinate  traverse. — When  the  line  is  unimportant  and  few  features  present 
themselves  to  be  noted,  an  auxiliary  plane  table  oriented  by  a  declinatoire  or  a  transit, 
fitted  with  stadia  wires,  may  be  employed. 

When  this  method  is  pursued  with  a  second  table  the  forward  rod  station  is  not 
occupied,  but  another  is  chosen  in  advance  of  it,  from  which  it  can  be  seen  where  the 
instrument  is  set  up  and  oriented  with  the  declinatoire.  Sighting  the  alidade  to  what 
is  now  the  back  station,  the  distance  is  read  and  plotted  along  the  edge  of  the  ruler, 
and  the  point  so  determined  represents  the  one  occupied  by  the  table. 

The  pivot  on  which  the  declinatoire  needle  rests  should  be  examined  frequently 
as  the  least  roughness  will  cause  the  needle  to  drag  and  introduces  serious  deflections 
in  azimuth. 

All  traverse  lines  should  start  and  end  at  well-determined  points.  This  will  serve 
to  check  the  accuracy  of  the  work.  If  the  closing  error  is  not  too  large,  the  line  should 
be  adjusted  by  distributing  it  throughout  its  length.  The  line  is  run  on  a  spare  sheet 
when  an  auxiliary  table  is  used;  then  traced,  "swung  in,"  and  adjusted  between  the 
two  fixed  points. 

Determinations  for  hydrography. — Where  the  topography  surveyed  includes  the 
shore  line  of  a  body  of  water,  the  hydrographic  survey  of  which  is  intended  to  follow  the 
topographic  work,  as  in  the  Coast  and  Geodetic  Survey,  it  is  the  duty  of  the  topographer 
to  locate  and  determine  the  shore  signals,  and  it  is  only  necessary  to  state  that  they  should 
be  so  placed  as  to  furnish  the  hydrographic  party  with  as  many  points  as  is  desirable  for 
the  determination  of  positions  on  the  water. 

Natural  or  artificial  objects  along  the  shore,  or  in  plain  sight  from  the  water,  such 
as  fence  ends,  rocks,  prominent  houses,  etc. ,  should  be  determined  and  marked  upon 
the  sheet. 

Lines  to  buoys  and  other  permanent  floating  objects  at  anchor  should  be,  as  far  as 
practicable,  taken  at  the  same  stage  of  the  tide,  or  direction  of  current. 

The  mean  low- water  mark  should  be  delineated,  and  when  it  is  beyond  the  reach  of 
the  plane-table  and  presents  no  marked  points  for  determination,  or  is  of  a  character 
that  will  not  permit  the  use  of  the  instrument — as  along  the  swampy  shores  in  the 


324 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


South,  where  the  muddy  shoals  extend  far  seaward,  and  among  the  shifting  quicksands 
of  our  great  estuaries  and  bays — it  may  be  left  to  be  traced  by  the  work  of  the  hydro- 
graphic  parties.  The  channels  through  mud  flats  of  this  character  should  be  indicated, 
however,  if  only  approximately,  by  cuts  and  tangents,  or  the  determination  of  stakes 
at  the  turning  points.  Where  the  fall  of  the  tide  exposes  rocks  and  ledges,  shingle 
beaches,  etc.,  their  character  and  extent  should  be  delineated  and  distinguished  from 
the  sandy  beaches,  as  these  features  are  most  difficult  and  laborious  for  the  hydro- 
graphic  survey  to  represent. 

High-water  and  storm-water  line. — In  tracing  the  shore  line  on  an  exposed  sandy 
coast  care  should  be' taken  to  discriminate  between  the  average  high-water  line  and  the 
storm- water  line. 

Determination  of  inaccessible  points. — On  a  precipitous  coast,  where  the  shore  line  is 
inaccessible  and  can  not  be  determined  by  ordinary  methods,  the  salient  features  are 
located,  when  occupying  commanding  stations,  by  observing  the  vertical  angles  upon 
them,  and  drawing  direction  lines  to  them.  Then  using  the  elevation  of  each  station 
as  a  base  the  distance  to  each  feature  is  computed  and  platted. 

The  same  method  applies  to  outlying  rocks,  and  is  often  employed  where  there  is 
any  doubt  of  their  being  identified  from  different  places. 

Large-scale  surveys. — As  has  been  previously  stated,  i-ioooo  and  1-20000  are  the 
scales  customarily  used  in  the  execution  of  the  topographic  work  of  the  Coast  and  Geo- 
detic Survey,  as  they  are  the  ones  best  suited  for  the  charting  of  the  coast  line  and 
harbors  of  the  United  States. 

Other  surveys  for  special  purposes  have  been  made  from  time  to  time  on  scales 
both  larger  and  smaller,  and  the  field  practice  has  been  modified  according  to  the  require- 
ments of  the  scale  used. 

A  topographic  survey  of  the  District  of  Columbia  outside  the  thickly  populated 
limits  of  the  city  of  Washington  was  made  between  the  years  of  1880  and  1891  on  a 
scale  of  1-4800. 

The  methods  pursued  are  here  described,  as  they  are  typical  of  other  surveys  on  a 
large  scale. 

Based  on  a  sufficiently  minute  triangulation,  the  plane-table  and  stadia,  wye  level, 
and  rod  were  used  for  all  determinations  of  details.  The  relief  was  elaborately  indicated 
by  contour  intervals  of  5  feet.  The  datum  plane  is  the  same  as  used  by  the  engineer 
department  of  the  District,  on  which  is  based  all  the  levels  used  for  grades  of  streets  and 
sewers  in  the  city  of  Washington,  the  survey  being  made  for  the  purpose  of  extending 
streets  and  avenues  beyond  the  city  limits. 

From  this  datum,  along  all  roads,  avenues,  and  railroads,  and  where  roads  were 
infrequent,  across  country,  lines  of  level  were  run,  and  after  careful  checking  in  the 
usual  manner  bench  marks  were  placed  in  position  convenient  to  all  parts  of  the  region. 

The  plane-table  stations  were  established  so  as  to  easily  overlook  every  part  of  the 
field  and  so  close  together  that  each  was  surrounded  by  the  others  within  the  range  of 
a  single  reading  of  the  stadia  rod. 

The  mode  of  procedure  was  as  follows: 

The  plane-table  was  placed  in  position  by  a  graphic  solution  of  three-point 
problem.  At  the  same  time  the  height  of  the  level  was  determined  above  some  near 
bench  mark  and  the  target  of  the  level  rod  fixed,  so  that  when  it  was  in  the  line  of  sight 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  325 

of  the  level  the  bottom  of  the  rod  would  rest  on  the  ground  where  the  elevation  corre- 
sponded to  that  of  some  contour.  The  level  rodsman  then  began  his  journey  along  this 
imaginary  horizontal  line,  holding  the  rod  for  the  observation  of  the  levelman  at  each 
noticeable  change  in  the  configuration  of  the  ground.  The  levelman  directed  the  rods- 
man  by  signals  at  each  point  until  the  rod  was  in  position  on  the  contour  line,  when  the 
stadia  rod  was  substituted  and  its  distance  read  and  plotted  on  the  plane-table  sheet. 
The  rodmen  followed  the  contour  line  in  both  directions  from  the  table  as  far  as  the 
stadia  rod  could  be  conveniently  read.  Generally  two  and  sometimes  three  contours 
were  run  from  one  level  station,  and  on  their  completion  a  turning  point  was  fixed  and 
the  level  shifted  to  higher  or  lower  ground,  as  the  circumstances  required. 

A  survey  of  Craney  Island,  Virginia,  was  made  in  the  same  manner  on  a  scale  of 
1-1200. 

RAPID   SURVEYS. 

Military  reconnaissance. — In  almost  every  field  of  operations,  from  the  commence- 
ment of  the  civil  war  to  its  close,  the  plane-table  was  used. 

Until  this  time  very  little  was  known,  save  in  theory,  of  the  value  of  the  plane-table 
as  a  reconnoitering  instrument,  and  all  the  officers  engaged  in  the  work  testify  that,  for 
rapidity  and  accuracy  in  the  execution  of  military  reconnaissance,  it  is  more  effective 
than  any  other  instrument. 

The  system  usually  adopted,  in  default  of  triangulation,  was  to  measure  a  base 
with  an  ordinary  chain  and  to  do  triangulation  with  the  plane-table. 

In  detailed  surveys  for  the  Army,  where  a  topographer  averages  from  i  to  3  square 
miles  a  day,  on  large  scales  a  chained  base  of  from  one-half  to  three-quarters  of  a  mile 
for  the  survey  of  an  area  of  25  square  miles  is  found  sufficient. 

At  Chattanooga,  from  two  different  bases  of  about  half  a  mile  each,  plotted  on 
separate  sheets,  and  carefully  measured  once  with  a  common  20- meter  chain,  the 
same  chain  being  used  to  measure  both  bases,  after  considerable  intermediate  plane- 
table  triangulation  carried  on  by  two  officers,  two  objects  were  determined  2j^  miles 
apart,  common  to  both  sheets,  which  were  on  a  scale  of  i-ioooo,  and  the  discrepancy 
was  but  about  15  meters.  Many  other  points  of  junction  indicated  this  to  be  the  maxi- 
mum error.  In  this  case  the  leaves  were  mostly  off  the  trees  and  the  hills  afforded 
good  points.  The  sheets  covered  about  20  square  miles  each.  At  Nashville  there 
was  a  discrepancy  of  about  10  meters  in  2  miles. 

At  other  times,  when  the  character  of  the  country  or  the  pressure  of  time  did  not 
admit  of  the  measurement  of  a  preliminary  base  and  plane-table  triangulation,  the 
work  was  commenced  by  starting  from  a  single  point  and  extended  by  linear  measure- 
ment with  the  chain  or  stadia,  intersections  from  the  ends  of  the  chained  lines  being 
taken  to  determine  objects,  which,  as  the  work  progressed,  could  also  be  used  as  checks 
upon  the  chaining.  Where  circumstances  permitted,  an  occasional  return  with  the 
chain  to  a  back  point,  either  to  close  a  series  of  lines  upon  it  or  to  start  afresh,  was 
resorted  to.  This  work  was  generally  carried  on  over  roads  and  the  interior  filled  in  by 
sketching  and  intersections  as  far  as  practicable.  Some  of  the  tests  of  this  latter  work, 
where  the  operations  of  two  officers  joined,  were  remarkably  close. 

A  very  efficient  topographic  officer  estimates  that  with  the  usual  number  of  hands 
and  a  good  sketcher  to  aid,  in  a  country  of  average  variety  of  detail,  in  which  all  the 


326  COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

houses,  prominent  barns  and  outbuildings,  streams,  roads,  general  outline  of  woods,  and 
approximate  curves  are  to  be  shown,  on  a  scale  of  i-ioooo,  an  area  of  between  2  and  3 
square  miles  can  be  filled  in  daily,  with  sufficient  accuracy  for  military  purposes. 

This  rapidity  of  work,  however,  could  not  be  expected  in  or  near  towns  or  populous 
districts.  It  is  doubtful  if,  under  average  conditions,  the  work  would  be  more  than  one- 
half  this  amount. 

In  some  thickly  wooded  sections  and  where  time  is  limited,  it  has  been  found 
advisable  to  run  the  main  roads  with  the  plane  table  and  fill  in  with  the  compass,  which 
is  more  rapid  but  less  accurate  than  where  the  entire  work  is  done  with  the  plane  table 
alone.  The  usual  method  employed  where  these  methods  were  combined,  was  as  follows: 
Where  the  army  was  stationary,  or  moving  leisurely,  one  main  road  was  run  with  the 
plane  table,  the  operator  being  accompanied  by  assistants  well  practiced  in  the  use  of 
the  compass.  Upon  arriving  at  any  important  road  or  water  course  an  assistant  was 
sent  to  the  right  and  left,  starting  from  a  plane-table  point,  determined  by  the  chaining, 
and  running  as  far  as  was  requisite  and  then  returning  to  the  main  road  again  to  repeat 
the  operation,  the  compass  notes,  of  course,  being  kept  in  a  book  prepared  for  the  pur- 
pose. Prominent  points  determined  by  the  plane  table  were  used  as  checks  in  the 
compass  work.  The  intervening  topography,  where  no  compass  or  plane-table  work 
had  been  done,  was  sketched  in  by  the  chief  of  the  party,  in  which  accurate  pacing 
became  of  great  value. 

With  compass  and  notebook. — Plane-table  methods  can  be  utilized  to  advantage 
when  compass,  pencil,  notebook,  and  ruler  are  the  substitutes  for  an  instrumental  outfit. 
The  book  serves  as  the  sheet  and  board  combined,  and  the  ruler,  as  it  was  in  the  early 
days  of  the  art,  becomes  the  alidade.* 

Photogrammetry .\ — In  the  topographic  reconnaissance  made  for  the  Alaska  Bound- 
ary Survey  by  the  Coast  and  Geodetic  Survey,  the  camera  with  constant  focal  length 
has  been  used  as  an  adjunct  to  the  small  mountain  plane  table.  The  latter  was 
used  to  plot  the  shore  line  and  adjacent  topography,  also  to  determine  as  many  peaks 
of  the  interior  country  as  possible  by  the  intersection  of  lines  of  direction.  All  camera 
stations  were  determined  geographically  and  hypsometrically,  and  plotted  upon  the 
plane-table  sheet.  The  topographic  details  beyond  the  reach  of  the  plane-table  were 
added  to  the  map  in  the  Office  by  the  photogrammetric  methods. 

The  rugged  mountains  of  southeast  Alaska  appear  particularly  well  adapted  for 
this  mode  of  procedure,  as  identical  points  can  be  readily  picked  out  from  different  pan- 
orama views,  owing  to  the  characteristic  shapes  of  the  mountain  peaks,  snow  fields, 
glaciers,  etc. 

Periods  of  fair  weather  are  also  very  short  and  of  rare  occurrence  in  that  locality, 
and  a  great  deal  of  topographic  material  can  be  gathered  photographically  in  a  short 
time,  which  when  plotted  will  cover  a  large  territory  if  a  sufficient  number  of  reference 
points  on  the  views  have  been  located  instrumentally. 

The  plotting  proper  can  be  carried  out  to  any  degree  of  minuteness  and  detail;  the 
only  requirement  is  that  a  sufficient  number  of  camera  stations  shall  have  been  occupied 

*See  "  Sketching  without  instruments,"  in  Topography,  Drawing,  and  Sketching,  by  Lieut.  Henry 
A.  Reed,  U.  S.  Army,  1886. 

fSee  United  States  Coast  and  Geodetic  Survey  Report,  1893,  Appendix  3,  and  Report  for  1897, 
Appendix  10. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  337 

to  fully  cover  the  territory  in  question,  so  that  every  topographic  feature  of  prominence 
has  been  seen  or  photographed  from  at  least  two  stations. 

By  this  application  of  photogrammetry  the  plane-table  methods  of  determining 
topographic  details  are  extended  to  the  Office,  inasmuch  as  the  same  features  are 
selected  from  the  panorama  views  and  plotted  geographically  which  would  have  been 
located  by  the  plane-table.  But  the  actual  time  spent  in  the  field  is  reduced  at  the 
expense  of  the  time  needed  for  office  work. 

Survey  in  advance  of  triangulation. — Where  it  is  necessary  to  make  a  topographic 
survey  in  advance  of  the  determination  of  points  by  triangulation,  a  reconnaissance  is 
first  made  for  the  location  of  a  base  line  and  selection  of  points  to  be  determined  with 
the  plane  table. 

The  base  is  measured  with  sufficient  accuracy  and  conveniently,  with  a  steel  tape 
which  has  been  compared  with  a  standard  at  a  fixed  tension,  and  to  one  end  of  which  is 
attached  a  spring  balance  to  secure  the  same  tension  during  measurement.  The  suc- 
cessive lengths  are  marked  by  lines  cut  on  copper  tacks  driven  in  wooden  stubs  firmly 
set  in  the  ground.  The  temperature  is  noted  at  frequent  intervals  as  the  work  progresses, 
and  the  corrections  are  applied  to  the  length  of  the  base  when  completed. 

The  base  is  then  properly  located  on  the  sheet  in  reference  to  the  area  to  be 
embraced  and  its  length  carefully  set  off.  It  is  well  at  the  same  time  to  mark  in  three 
or  four  different  parts  of  the  sheet  lengths  of  i  ooo  meters  for  the  purpose  of  determin- 
ing at  any  time  the  true  scale  of  the  sheet,  variable  by  the  different  hygrometric  condi- 
tions of  the  atmosphere. 

Signals  having  been  erected  at  the  selected  points,  the  extremes  of  the  base  are 
occupied  with  the  table  and  the 'points,  as  far  as  may  be  reached  with  good  intersections, 
determined  from  them  and  lines  of  direction  drawn  to  all  the  points  visible,  to  serve  as 
checks  upon  their  determination  from  other  points  furnishing  directions  for  good  inter- 
sections. The  survey  then  proceeds  as  usual. 

It  is  well  at  the  beginning  of  work  to  draw  (using  the  declinatoire)  the  magnetic 
meridian,  at  some  determined  point  near  the  middle  of  the  sheet  for  the  purpose  of  put- 
ting the  table  in  approximate  position  at  any  station  with  the  declinatoire.  The  manner 
of  doing  this  is  described  elsewhere. 

Before  finishing  the  field  work  it  is  important,  when  the  sheet  has  no  projection,  to 
provide  data  for  drawing  a  true  north  and  south  line.  This  is  done  by  drawing  from 
a  point  upon  the  sheet,  when  the  table  is  in  position,  a  line  in  the  vertical  plane  through 
Polaris  and  the  point  occupied  and  recording  the  time  of  observation.  The  azimuth  of 
the  star  at  that  time  being  known,  a  true  north  and  south  line  can  accordingly  be  set  off. 

If  a  small  transit  instrument  is  at  hand  and  carefully  adjusted  for  movement  in 
vertical  plane,  an  assistant  with  a  lantern  can  be  located  where  the  vertical  plane  through 
Polaris  and  the  point  occupied  intersects  the  ground,  at  as  great  a  distance  from  the 
point  as  the  ground  will  admit  within  the  limit  of  communication  by  light  signals. 
When  such  a  position  is  marked  the  direction  from  the  point  occupied  may  be  deter- 
mined by  daylight. 

If,  in  the  absence  of  a  transit,  the  alidade  has  not  vertical  range  sufficient  to  observe 
Polaris,  an  illuminated  plumb  line  may  be  used  for  the  alignment. 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 
OFFICE   WORK. 

All  the  topographic  features  of  a  survey  should  be  drawn  in  pencil  upon  the  sheet 
in  the  field,  while  they  can  be  seen.  Sketching  and  plotting  in  the  office  from  notes, 
unless  the  country  be  near  at  hand  for  ready  reference  in  case  of  doubt  or  defective  data, 
is  objectionable.  When  this  is  unavoidable,  the  sketches  should  be  transferred  to  the 
sheet  as  soon  as  possible  after  being  made,  while  fresh  in  the  mind  of  the  person  by  whom 
they  were  made,  and  by  whom  they  should  be  plotted.  Days  which,  from  inclemency 
of  the  weather,  are  unfavorable  for  out-of-door  work  should  be  allotted  to  this  purpose, 
and  advantage  should  be  taken  of  them,  also,  for  retouching  any  details  of  the  sheet 
which  may  have  become  indistinct,  as  it  is  very  important  that  they  should  not  be  left 
indefinite  or  become  obliterated;  for  when  the  inking  is  done,  as  it  generally  is,  at  a 
distance  from  the  field  of  operations,  the  necessity  for  this  care  is  obvious.  Nos.  4 
and  5  pencils  are  good  for  this  purpose,  for  which  very  hard  or  very  soft  and  black 
pencils  are  equally  unsuited. 

In  the  inking  of  a  topographic  sheet  three  requisites  to  its  proper  appearance 
when  finished  should  be  borne  in  mind — clearness,  neatness,  and  uniformity. 

The  lines  and  objects  should  be  clear  and  sharply  defined,  nothing  being  left  obscure 
or  doubtful;  the  paper  should  be  kept  unsoiled,  and  erasures  avoided  as  far  as  possible, 
and  the  style  and  strength  of  the  drawing  should  be  the  same  throughout.  It  is  an 
important  matter  that  an  easy  and  natural  appearance  should  be  given  to  the  sheet,  for,  as 
before  remarked,  a  mere  rigid  adherence  to  conventional  signs  is  not  all  that  is  neces- 
sary; while  there  should  be  no  deviation  in  this  respect,  at  the  same  time  the  drafts- 
man should  strive  to  represent  the  country.  There  is  a  great  difference  with  regard  to 
this  among  topographers.  Two  correct  sheets  of  the  same  section  of  ground,  executed 
by  different  persons,  may  be  inked,  and  while  one  will  have  a  stiff  and  ungraceful  look, 
the  other  will  appear  artistic  and  natural,  giving  at  once  the  impression  of  a  true  repre- 
sentation of  the  country  surveyed. 

Office  work  should  not  be  commenced  until  the  topography  is  entirely  completed,  as 
no  inked  or  partially  inked  sheet  should  ever  be  used  in  the  field.  Sometimes,  for  the 
special  examination  of  old  work,  or  for  the  insertion  of  some  recent  artificial  or  natural 
changes,  this  becomes  necessary,  but  there  is  always  a  risk  of  injuring  an  inked  sheet 
by  exposure  to  the  weather  or  by  using  it  upon  a  plane  table. 

The  inking  should  begin  with  the  high  and  low  water  lines.  The  high-water  line 
or  shore  line  proper  should,  in  all  cases,  be  full  and  black,  the  heaviest  line  on  the 
sheet,  and  in  this,  as  in  all  the  rest  of  the  ink  work,  the  lines  of  the  surveyor  should 
be  strictly  adhered  to. 

The  topography  as  drawn  in  the  field  is  supposed  to  be  correct  when  the  sheet  is 
finished,  and  no  office  amendments  or  changes  are  admissible.  The  low- water  line  is 
drawn,  not  so  full  as  the  former,  but  clear,  black,  and  uniform,  consisting  of  a  dotted 
line  for  sand  and  mud  and  the  conventional  sign  where  it  is  formed  by  shells,  rocks, 
or  coral  reefs. 

Neither  the  inner  border  of  a  marsh  nor  a  shoal  covered  at  high  tide  has  a  distinct 
continuous  line  to  mark  its  limits,  each  being  represented  in  its  proper  form  and  within 
its  area  by  its  conventional  sign  only,  but  the  shape  should  be  well  and  correctly 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  329 

defined.  All  objects  between  high  and  low  water,  covered  at  full  tide,  should  be  repre- 
sented less  boldly  than  the  other  features  on  the  sheet,  but  not  faintly  or  indefinitely. 

The  roads  should  be  inked  plainly  and  evenly,  with  their  sides  parallel,  except 
where  the  survey  shows  a  deviation  from  the  general  width.  Main  thoroughfares  when 
fenced  are  drawn  with  a  full  line,  subordinate  roads  where  fenced  should  be  shown  by 
the  usual  sign,  and  where  there  is  ro  inclosure  a  line  of  dashes  should  indicate  the  road- 
side, and  then  should  follow  the  fences  and  houses.  In  drawing  the  latter,  care  must 
be  taken  that  the  corners  and  angles  exhibit  a  sharp,  clear  outline,  which  adds  much  to 
the  appearance  of  the  sheet. 

The  general  skeleton  of  the  survey  being  now  completed,  the  contours  are  drawn 
with  a  bold,  uniform,  plain  red  line,  without  break,  over  all  the  other  work,  following 
accurately  the  full  range  of  level  of  each  of  the  contours  on  the  sheet. 

After  this  comes  the  general  filling  in,  by  conventional  signs,  of  sand,  marsh,  grass, 
cultivation,  orchards,  rocks,  hachures,  etc.  Some  practice  is  needed  to  execute  the  sand 
work  regularly  and  neatly.  It  should  never  be  done  hurriedly,  though  of  course 
rapidity  in  this  respect  follows  practice.  The  lines  representing  marsh,  and  the  delin- 
eation of  grass  on  the  fast  ground,  should  always  run  in  the  same  direction  over  the 
whole  sheet  and  be  parallel  to  the  top  of  the  sheet  and  the  title.  The  appended  draw- 
ings (Illustratious  17,  18,  19,  20,  and  21)  give  the  conventional  signs  as  adopted  by  and 
now  used  by  the  Coast  and  Geodetic  Survey. 

The  most  difficult  part  of  the  inking  for  a  beginner  is  the  lettering,  which  now 
follows,  and  for  which  samples  are  given  (Illustration  22).  It  is  expected  that  every 
topographer  shall  have  learned  to  draw  sufficiently  well  to  ink  his  sheet  in  a  clear  and 
distinct  manner  and  letter  it  with  some  regard  to  neatness  and  graphic  effect,  as  the 
appearance  of  an  otherwise  well-inked  sheet  is  marred  by  careless  or  indifferent  lettering. 

The  location  of  the  names  upon  the  sheet  should  be  such  as  not  to  cover  or  oblit- 
erate any  detail  or  feature  of  the  survey,  and  the  letters  should  be  put  on  neatly  and 
gracefully,  and  in  point  of  size  and  form  according  to  the  specimens  furnished.  The 
title  should  follow,  with  such  notes  as  may  be  necessary  to  explain  any  peculiarity 
of  the  sheet  or  survey.*  This  title  and  lettering  should,  as  far  as  practicable,  be  so 
placed  that  when  the  sheet  is  held  with  the  top  (the  north  end  of  the  map)  from  you 
it  can  be  easily  read;  in  other  words,  as  nearly  parallel  to  the  top  or  upper  end  of  the 
sheet  as  the  nature  of  the  work  will  admit.  All  names  well  established  and  recognized 
in  a  neighborhood,  both  general  and  local,  should  be  collected  during  the  survey,  and 
their  correct  orthography  ascertained,  and  in  case  of  any  doubtful  or  disputed  orthog- 
raphy a  report  should  be  made  giving  any  traditions  or  authorities  which  bear  upon 
the  subject.  No  illuminated  or  German  text,  old  English,  or  what  is  known  as  "fancy 
printing,"  should  be  indulged  in,  a  strict  adherence  to  simplicity  being  required. 

The  minutes  of  the  parallels  of  latitude  and  meridians  of  longitude  should  be 
marked  in  figures  at  the  upper  and  right-hand  ends,  respectively,  the  degrees  on  the 
center  parallel  and  center  meridian  only. 

When  buoys  are  determined  by  the  topographer,  and  their  names,  colors,  numbers, 
or  kind  are  known,  they  should  be  placed  on  the  sheet  and  so  marked. 

*  The  topographers  in  the  Coast  and  Geodetic  Survey  are  required  to  write  the  title  and  notes  on 
a  separate  sheet  of  paper  and  attach  it  to  the  plane  table  sheet.  This  portion  of  the  lettering  is  done 
at  the  Office. 


330 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


The  triangulation  points  should  be  surrounded  by  a  small  red  triangle.  Barns, 
houses,  prominent  trees,  and  other  objects  determined  by  the  plane  table  that  may  be 
used  as  points  of  reference  in  making  additions  to  the  sheet  subsequent  to  the  survey 
should  be  indicated  by  a  small  blue  circle. 


TABLES   AND 

Table  for  reducing  readings  of  inclined  sights  on  a  rod  held  perpendicular  to  the  line  of  sight. 


Hypothenuse 

Angle 

100  meters 

200  meters 

300  meters 

400  meters 

500  meters 

5° 

99.62 

199.24 

298.86 

398.  48 

498.  10 

10° 

98.48 

196.96 

295-44 

393-  92 

492.  40 

15° 

96.59 

193-  19 

289.  78 

386.37 

482.96 

20° 

93-97 

187.  94 

281.91 

375-88 

469.85 

25° 

90.63 

181.26 

271.  89 

362.  52 

453-  15 

30° 

86.60 

173.21 

259.  81 

346.  41 

433-  oi 

35° 

81.92 

163.  83 

245-  75 

327.  66 

409-  58 

40° 

76.60 

153-  21 

229.  81 

306.  42 

383-  02 

45° 

70.71 

T4I.42 

212.  13 

282.  84 

353-55 

When  it  is  desired  to  use  the  preceding  table,  a  sight  must  be  attached  to  the  rod  or 
the  proper  position  of  the  rod  left  to  the  judgment  of  the  rodsman.  The  usual  and 
safer  way  is  to  have  the  rod  held  vertical  for  all  readings.  There  are  then  two  corrections 
to  be  applied,  one  to  reduce  the  inclined  distance  to  a  horizontal  one  and  one  for  the 
oblique  view  of  the  rod. 

The  equation  for  reducing  the  readings  is: 

Horizontal  distance =r  cosa  v-\-(c-\-f)  cos  v 

Where  r=  reading  of  vertical  rod; 

v= angle  of  elevation  or  depression; 
c=  distance  of  object  glass  to  center  of  instrument; 
f=  focal  length  of  telescope. 

The  following  table  gives  the  coefficient  of  reduction  by  which  the  rod  reading  is 
to  be  multiplied.  It  is  based  on  the  assumption  that  c-\-fis  to  be  added  to  the  result  to 
obtain  the  distance  to  the  center  of  the  instrument. 

Example:  Given  an  angle  of  elevation  or  depression  8°  10'  and  the  reading  of  the 
inclined  sight  on  vertical  rod  =173.1  meters. 
From  the  table: 

Factor  for  i     meter  for  8°  io7  multiplied  by  100=97.  98  meters. 
"  7        "       "    "     "  "  "     10=68.59       " 

"         "3        "       "    "     " =  2.94       " 

"         "  o.i      "       "    "     "     =     .09       " 


Horizontal  distance 169.  60 

To  which  c -\-f  is  to  be  added. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL. 


331 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  a  vertical  rod  to  horizontal 

distance.* 


Angle  of 
inclina- 
tion 

Horizontal  projection  of 

i  m. 

2  m. 

3m. 

4  m. 

5m. 

6  m. 

7m. 

8  m. 

9  m. 

0°  IC/ 

2«y 

3c/ 
4c/ 
5^ 

•99999 
•  99997 

•  99979 

I.  99998 

I-  99993 
i.  99984 

i.  99973 
i.  99957 

2-  99997 
2.  99990 

2.  99977 
2.  99959 
2.  99936 

3-  99997 
3-  99986 
3.  99969 
3-  99946 
3-  99915 

4-  99996 
4-  99983 
4-  99962 
4-  99932 
4-  99894 

5-  99994 
5-  9998o 
5-  99954 
5-  99919 
5.99873 

6.  99994 
6.  99977 
6.  99946 
6.  99905 
6.  99852 

7-  99993 
7-  99973 
7-  99939 
7.  99892 

7-99831 

8.  99993 
8.  99970 
8.  99932 
8.  99878 
8.  99810 

I°OC/ 

•  99970 

i.  99939 

2.99909 

3-  99878 

4.  99848 

5-  998i7 

6.  99787 

7-  99757 

8.  99726 

10' 
2C/ 

3°; 

4c/ 
So' 

•  99959 
.99946 

•  99932 
•  999J5 
.99908 

1.99917 
i.  99891 
1.99863 
i.  99831 
i.  99801 

2-  99875 
2.  99838 

2-  99794 
2.  99746 

2-  99693 

3-  99834 
3-  99783 
3-99725 
3-  99659 
3-  99590 

4-  99793 
4.  99729 

4-  99657 
4-  99572 
4-  99488 

5-  99752 
5-  99676 
5-  99589 
5-  99489 
5-  99386 

6.99711 
6.  99622 
6.  99520 
6.  99406 
6.  99284 

7-  99669 
7-  99568 
7-  99452 
7-  99323 
7.  99182 

8.99628 
8.  99514 
8.  99384 
8.  99239 
8.99080 

2°  CX/ 

.99878 

i.  99756 

2.  99635 

3-  99513 

4-  9939  1 

5-  99269 

6.  99147 

7.  99025 

8.98904 

IC/ 
2</ 

30' 
4c/ 
50' 

•  99857 
•  99834 
.  99810 
.99784 
•  99756 

1.99714 
i.  99669 
i  .  99620 
1.99568 
I-995II 

2-  99571 
2-  99503 
2.  99429 

2.99351 
2.  99267 

3-  99428 
3-  99337 
3-  99239 
3-  99135 
3-  99023 

4.  99285 
4.99171 
4-  99049 
4.  98918 

4.98778 

5-  99142 
5.99006 

5-  98859 
5-  98702 
5-  98534 

6.  99000 
6.  98840 
6.  98669 
6.98485 
6.  98290 

7-  98857 
7-  98675 
7-  98479 
7.  98268 
7.  98046 

8.  98714 
8.98509 
8.  98289 
8.98053 
8.  97802 

3°  oo' 

.  99726 

i.  99452 

2.  99178 

3.98904 

4.  98630 

5-  98357 

6.98083 

7.97809 

8.  97635 

IC/ 

2c/ 
3c/ 
4c/ 
5^ 

•99695 
.  99662 
.  99627 
•99591 
•  99553 

i.  99390 
1.99324 

i.  99255 
i.  99182 
i.  99106 

2.  99085 
2.  98986 
2.  98882 
2.  98773 
2.  98659 

3.98780 
3.98648 
3-  98509 
3-  98364 
3.98212 

4-  98474 
4-  98309 
4-  98136 
4-  97955 
4-  97765 

5-  98169 
5-  97972 
5-  97764 
5-  97546 
5-  973i8 

6.  97865 
6-  97634 
6-  97391 
6.97137 
6.  96871 

7.  97560 
7.  97296 

7-  97019 
7.  96728 

7-96424 

8.  97255 
8.  96958 
8.  96646 
8.  96319 
8.  95978 

4°oc/ 

•99513 

i.  99027 

2.  98540 

3-  98054 

4-  97567 

5.97081 

6.  96595 

7.  96108 

8.95621 

IC/ 
2C/ 

3c/ 
4c/ 
50' 

•  99472 
•  99429 
•99384 
•  99338 
.  99290 

1.98944 
i.  98858 
1.98769 
1.98676 
i.  98580 

2.  98416 
2.  98287 

2.  98153 
2.  98014 
2.  97870 

3-  97888 
3-  977i6 
3-97537 
3-  97352 
3.  97160 

4.  9736o 

4.97I45 
4.  96922 
4.  96690 
4.  96450 

5-  96832 
5-  96574 
5-  96306 
5.  96028 
5-95740 

6.  96304 
6.  96003 
6.  95691 
6.  95366 
6.  95030 

7-  95776 
7-  95432 
7-  95075 
7-  94704 
7-  94320 

8.  95249 
8.  94862 
8.  94460 

8.  94043 
8.93611 

5°oc/ 

.99240 

i.  98481 

2.97721 

3-  96961 

4.  96202 

5-  95443 

6.  94683 

7-  93923 

8.93164 

IC/ 
2C/ 

3^ 

4c/ 
5^ 

.99189 
•99136 
.99081 
.99025 
.98967 

i.  98378 
i.  98272 
i.  98163 
i.  98050 
r.  97934 

2.  97567 
2.  97408 
2.  97244 

2-  97075 
2.  96901 

3-  96756 
3-  96544 
3-  96326 
3.  96100 
3-  95868 

4-95945 
4-  9568o 
4-  95407 
4-95125 
4-  94835 

5.95134 
5-94816 

5.94489 
5-  94150 
5.  93802 

6.  94323 
6.  93952 
6.  93570 

6.93175 
6.  92769 

7-  935" 
7-  93088 
7.  92652 
7.  92200 
7.  91736 

8.  92702 
8.  92224 

8.91733 
8.  91225 
8.  90703 

6°oc/ 

.98907 

i.  97814 

2.  96722 

3-  95630 

4-  94537 

5-  93445 

6.  92358 

7.  91260 

8.  90167 

IC/ 
2C/ 

y/ 

4C/ 

50' 

.  98846 

•  98783 
.  98718 
•  98652 
.98584 

i.  97692 
i.  97566 
i.  97436 
1.97304 
i.  97169 

2.96538 
2.  96349 
2-  96155 
2-  95956 
2-  95753 

3-  95384 
3-95I32 
3-  94873 
3-94609 

3-  94337 

4-  94230 
4-  93915 
4-  93591 
4-  9326i 
4.  92921 

5-  93077 
5-  92698 
5.  92310 

5.9I9I3 
5-91506 

6.91923 
6.  91481 
6.91029 
6.90566 
6.  90090 

7-90769 
7.  90264 
7-  89748 
7.89218 
7.  88674 

8.  89615 
8.  89048 
8.  88467 
8.  87870 
8.  87259 

7°oc/ 

•98515 

i.  97030 

2.  95544 

3.94059 

4-  92574 

5-  91089 

6.89604 

7.88119 

8.  86634 

*  Computed  by  J.  A.  Flemer,  Assistant,  Coast  and  Geodetic  Survey. 


332 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  a  vertical  rod  to  horizontal 

distance — Continued. 


Angle  of 
inclina- 
tion 

Horizontal  projection  of 

i  m. 

2  m. 

3  m.   ' 

4  m. 

5  ™. 

6  m. 

7  m. 

8  m. 

9  m. 

10' 
20' 
30' 

& 
& 

.98444 

.98371 
.98296 
.  98220 
.98142 

1.96888 
1.96742 
I.  96592 
1.96441 
I.  96285 

2-  95331 
2.95112 
2.  94889 
2.  94661 
2.  94427 

3-  93775 
3.93483 
3-  93i85 
3-  92881 
3-  92570 

4.  92218 
4.  91854 
4.  91481 
4.  9IIOI 
4.  90712 

5.90662 
5.90225 
5-  89777 
5-  89322 
5-  88855 

6.  89105 
6.  88596 
6.  88073 
6.  87542 
6.  86997 

7-  87549 
7.  86967 
7-  86370 
7-  85762 
7.85140 

8-85993 
8-85337 
8.  84667 
8.  83982 
8.  83282 

8°  ex/ 

.98063 

I.  96126 

2.94189 

3-  92252 

4-  90315 

5-  88378 

6.  86441 

7-  84504 

8.  82568 

IC/ 
20' 
30; 

40' 
5o/ 

.97982 
.97899 
•  97815 
•  97729 
.  97642 

1.95964 
I-  95798 
I-  95630 

1-95459 
i.  95284 

2.  93946 
2.  93698 
2.  93446 
2.  93188 
2.  92926 

3.91928 

3-  91598 
3.91261 

3-  9091  8 
3.90568 

4.  89910 

4-  89497 
4.  89076 
4.  88647 
4.  88209 

5.  87892 
5-  87396 
5.  86891 
5-  86377 
5-  85851 

6.  85874 
6.  85296 
6  .  84707 
6.  84106 
6.  83493 

7-  83856 
7.83196 
7.  82522 
7.  81836 
7.81134 

8.  81839 
8.  81096 
8.  80337 

8.  79565 
8.  78777 

9°  oo' 

•  97553 

I.  95106 

2.  92658 

3.90211 

4-  87764 

5.85317 

6.  82870 

7-  80423 

8-  77975 

lO' 
2C/ 

3o/ 
40' 
So' 

.  97462 
•  97370 
•  97276 
.97180 
•97083 

i.  94924 
1.94740 
L94552 
i.  94361 
i.  94166 

2.  92386 
2.  92IIO 
2.  91828 
2.  91542 
2.  91250 

3-  89848 
3-  89480 
3.  89104 
3.  88722 
3-  88333 

4.87310 
4.  86849 
4.  86379 
4.  85902 
4.  85416 

5-  84772 
5-  84219 
5-  83655 
5-  83083 
5-  82499 

6.  82234 
6.  81589 
6.  80931 
6.  80263 
6.  79583 

7-79696 
7-  78959 
7.  78207 

7-  77444 
7.  76667 

8-  77159 
8.  76328 

8-  75483 
8.  74624 
8.  73750 

10°  Of/ 

.96985 

1.93970 

2.90954 

3-  87938 

4.  84923 

5.81907 

6.  78892 

7-  75876 

8.  72861 

IC/ 
2C/ 

3o/ 
407 
5^ 

.96884 
.96782 
.96679 
.96574 
•  96467 

1.93769 
i.  93565 
I-  93358 
i.  93148 
i.  92934 

2.90653 

2.  90347 
2.90037 
2.  89721 
2.  89402 

3-  87537 
3-  87129 
3.  86716 
3-  86295 
3-  85869 

4.  84421 
4-  83912 

4-  83395 
4.  82869 
4-  82336 

5-  81306 
5-  80695 
5.80074 

5-  79443 
5-  78803 

6.  78190 
6.  77477 
6-  76753  ' 
6.  76017 
6.  75271 

7-  75074 
7-  74259 
7-  73432 
7-  72591 
7-  71738 

8.  71959 
8.  71042 
8.  70111 
8.69165 
8.  68206 

11°  CX/ 

•96359 

1.92718 

2.89077 

3-  85436 

4-  8i795 

5-  78i54 

6.  74513 

7.  70872 

8.  67232 

IC/ 
20' 
30' 

40' 
SO' 

.96249 
.96138 
.96025 

•959" 
•  95795 

i.  92498 
1.92276 
1.92051 
i.  91822 
1.91590 

2.  88748 
2.  88414 
2.  88076 
2.  87732 
2.87385 

3-  84997 
3-  84552 
3.  84101 

3-  83643 
3.  83180 

4-81247 
4.80690 
4.  80126 
4-  79553 
4-  78974 

5-  77496 
5.  76828 
5-  76152 
5-  75464 
5-  74769 

6.  73746 
6.  72966 
6.  72177 

6-  71375 
6.  70564 

7-  69995 
7.  69104 
7.  68202 
7.  67286 
7-  66358 

8.  66245 
8.  65242 
8.  64227 
8.63196 
8.62153 

12°  OC/ 

•  95677 

I.9I355 

2.  87032 

3.  82709 

4-  78386 

5-74063 

6.  69741 

7-  65418 

8.  61095 

IC/ 
2C/ 

30' 
40' 
50' 

•  95558 
•  95438 
•  95315 
•95192 
.95066 

i.  91116 
1.90876 
1.90631 
i.  90384 
1.90132 

2.86674 
2.86313 
2.  85946 
2-  85575 
2.  85199 

3.  82232 
3-81750 
3.81261 
3.80766 
3.80265 

4.  77790 
4.  77187 
4-  76576 
4-  75958 
4-  75332 

5-  73348 
5-  72625 
5-  71892 
5-7II50 
5-  70399 

6.68906 
6.  68062 
6.  67207 
6.  66341 
6.  65465 

7-  64464 
7-  63500 
7.  62522 

7-  61533 
7-  60532 

8.  60023 
8.58938 
8.57838 
8.  56724 
8-  55598 

13°  oc/ 

.94940 

1.89880 

2.  84820 

3-  79759 

4.74698 

5-  69638 

6.  64577 

7-595I6 

8.  54456 

10' 
207 

y/ 

40' 
So' 

.94811 
.94682 
•  94550 
.94417 
•94283 

1.89623 
i.  89364 
i.  89101 
1.88835 
1.88566 

2.  84434 
2.  84045 
2.  83651 
2.  83252 
2.  82849 

3-  79245 
3-  78726 
3.  78201 
3-  77669 
3-  77132 

4-  74056 
4-  73407 
4-  72751 
4.  72087 

4.7I4I5 

5.  68868 
5.68088 

5-  67301 
5-  66505 
5-65698 

6.  63679 
6.  62770 
6.61852 
6.  60922 
6.59981 

7-  58491 
7-  57452 
7-  56402 
7-  55339 
7-  54264 

8.  53302 
8-52133 
8.  50952 
8.49757 
8.  48548 

14°  oc/ 

-94M7 

1.88295 

2.  82442 

3-  76589 

4-  70736 

5-  64884 

6.  59031 

7.53179 

8.  47326 

APPENDIX  7.     A  PLANE  TABLE  MANUAL. 


333 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  a  vertical  rod  to  horizontal 

distance — Concluded. 


Angle  of 
inclina- 
tion 

Horizontal  projection  of 

i  m. 

2  m. 

3m. 

4  m. 

5  m. 

6  ni. 

7  m. 

8  m. 

9  m. 

10' 
20/ 

30/ 
40' 
50' 

.  94010 
•  93871 
•  93731 
•  93589 
.93446 

I.  88020 
I.  87742 
I.  87462 
1.87178 
I.  86892 

2.  82030 
2.81613 
2.  81192 
2.  80767 
2.  80338 

3.  76040 
3-  75484 
3-  74923 
3-  74356 
3-  73784 

4.  70050 
4-  69355 
4.  68654 

4-  67945 
4.  67229 

5.64060 
5-  63226 
5-  62385 
5-  61534 
5-60675 

6.  58070 
6.  67097 
6.56115 
6.55123 
6.54121 

7.  52080 
7.  50968 
7-  49846 
7.48712 
7-  47567 

8.46090 
8.  44840 
8.  43578 
8.  42302 
8.  41013 

I5°  Of/ 

•  93301 

I.  86602 

2.  79903 

3-  73204 

4-  66505 

5.598o6 

6.  53107 

7.  46408 

8.  397io 

i6°oo' 

.  92402 

I.  84805 

2.  77208 

3.  69610 

4.  62011 

5-  544H 

6.  46816 

7-  392i8 

8.  31620 

17°  ex/ 

•  91452 

I.  82904 

2.  74355 

3.65806 

4-  57258 

5-  48710 

6.  40161 

7-  31613 

8.  23065 

i8°oc/ 

.90451 

I.  80902 

2.71352 

3.  61803 

4-  52253 

5.42704 

6.  33154 

7-23605 

8.  14056 

19°  00' 

.  89400 

1.78800 

2.  68201 

3.57600 

4.  47001 

5-  36402 

6.  25802 

7.  15203 

8.  04603 

20°  oc/ 

.  88302 

I.  76604 

2.  64906 

3-  532o8 

4.  41510 

5-  29812 

6.  18114 

7.  06416 

7.  947i8 

334 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


TABLE  I. — Table  showing  th'e  height  in  feet  corresponding  to  a  given  angle  of  elevation 

and  a  given  distance  in  meters* 


Meters 

300 

400 

500 

600 

700 

800 

900 

1000 

IIOO 

I2OO 

1300 

1400 

1500 

1600 

1700 

1800 

I9OO 

2OOO 

Angle 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

i' 

0.3 

0.4 

0.6 

0.6 

0.8 

0.9 

I.O 

1.2 

1-3 

1-5 

i-7 

1.8 

2.0 

2.2 

2.3 

2-5 

2.7 

2.8 

2 

0.6 

0.8 

I.O 

1.2 

1-5 

1-7 

i-9 

2.1 

2.4 

2.6 

2.9 

3-1 

3-4 

3-7 

3-9 

4.2 

4-5 

4.7 

3 

0.9 

1.2 

i-5 

1.8 

2.2 

2-5 

2.8 

3-i 

3-4 

3-8 

4.2 

4.4 

4.8 

5-3 

5-6 

5-9 

6-3 

6.6 

4 

1.2 

i-5 

2.0 

2.4 

2.8 

3-2 

3-6 

4.1 

4-5 

4-9 

5-4 

5-8 

6-3 

6.8 

7.2 

7-6 

8.1 

8.6 

5 

1-5 

i-9 

2-4 

2.9 

3-5 

4-0 

4-5 

5-o 

5-5 

6.1 

6.6 

7-1 

7-7 

8-3 

8.8 

9-4 

9-9 

10.5 

6 

1.8 

2.3 

2.9 

3-5 

4-2 

4.8 

5-3 

5-9 

6.6 

7.2 

7-9 

8-5 

9-i 

9.8 

10.4 

II.  I 

ii.  7 

12.4 

7 

2.1 

2.7 

3-4 

4-1 

4-8 

5-5 

6.2 

6.9 

7.6 

8.4 

9-i 

9.8 

10.6 

11.4 

12.  I 

12.8 

13-5 

14-3 

8 

2-4 

3-i 

3-9 

4.6 

5-5 

6-3 

7-i 

7-9 

8.7 

9-5 

10.4 

ii.  i 

12.  O 

12.9 

13-7 

14-5 

15-3 

16.2 

9 

2.7 

3-5 

4-4 

5-2 

6.2 

7.0 

7-9 

8.8 

9-7 

10.7 

ii.  6 

12.5 

13.4 

14.4 

15-3 

16.2 

17.2 

18.  1 

10 

2.9 

3-8 

4-9 

5-8 

6.8 

7.8 

8.8 

9.8 

10.8 

ii.  8 

12.8 

13.8 

14.9 

J5-9 

16.9 

17.9 

19.0 

20.  o 

ii 

3-2 

4-2 

5-3 

6.4 

7-5 

8.6 

9-6 

10.7 

ii.  8 

13-0 

14.1 

iS-i 

16.3 

17-5 

18.6 

19.7 

20.8 

21.9 

12 

3.5 

4-6 

5-8 

6.9 

8.2 

9-3 

10.5 

11.7 

12.9 

14.1 

15-3 

16.5 

17.7 

19.0 

20.2 

21.4 

22.6 

23.8 

13 

3-8 

5-0 

6-3 

7-5 

8.8 

10.  I 

11.4 

12.6 

13-9 

15-2 

16.6 

17.8 

19.2 

20.5 

21.8 

23.1 

24.4 

25-7 

14 

4-1 

5-4 

6.8 

8.1 

9-5 

10.9 

12.2 

13-6 

15-0 

16.4 

17.8 

19.1 

20.  6 

22.0 

23-4 

24.8 

26.2 

27.6 

15 

4-4 

5-7 

7-2 

8.6 

10.2 

11.6 

I3-I 

14-5 

16.  o 

17-5 

19.0 

20.5 

22.  O 

23.6 

25.0 

26.5 

28.0 

29-5 

16 

4-7 

6.1 

7-7 

9-2 

10.8 

12.4 

13-9 

15-5 

17.1 

18.7 

20.3 

21.8 

23-5 

25-1 

26.7 

28.2 

29.9 

31-4 

17 

4-9 

6-5 

8.2 

9-8 

"•5 

13-1 

14.8 

16.5 

18.  i 

19.8 

21.5 

23.1 

24.9 

26.6 

28.3 

30.0 

31-7 

33-4 

18 

5-2 

6.9 

8.7 

10.4 

12.2 

13-9 

15-7 

17.4 

19.2 

21.  0 

22.8 

24-5 

26.3 

28.2 

29.9 

31.7 

33-5 

35-3 

19 

5-5 

7-3 

9-i 

10.9 

12.8 

14-7 

I6.5 

18.4 

20.2 

22.1 

24.0 

25.8 

27.7 

29.7 

31-5 

33-4 

35-3 

37-2 

20 

5-8 

7-7 

9-6 

«.  5 

13-5 

15-4 

»7-4 

19-3 

21.3 

23-3 

25.2 

27.2 

29.2 

31-2 

33-2 

35-1 

37-1 

39-1 

21 

6.1 

8.0 

10.  I 

12.  1 

14.2 

16.2 

18.2 

20.3 

22.3 

24.4 

26.5 

28.5 

30.6 

32.7 

34-8 

36.8 

38.9 

41.0 

22 

6.4 

8.4 

10.6 

12.6 

14.9 

17.0 

19.1 

21.2 

23.4 

25-5 

27.7 

29.8 

32.0 

34-3 

36.4 

38.5 

40.7 

42.9 

23 

6.7 

8.8 

ii.  i 

13-2 

15-5 

17-7 

20.0 

22.2 

24-4 

26.7 

29.0 

31-2 

33-5 

35-8 

38.0 

40.3 

42.5 

44.8 

24 

6-9 

9-2 

"•5 

13.8 

16.2 

18.5 

20.8 

23-1 

25-5 

27.8 

30.2 

32.5 

34-9 

37-3 

39-6 

42.0 

44-3 

46.7 

25 

7-  a 

9-6 

12.0 

14.4 

16.9 

19-3 

21.7 

24.1 

26.5 

29.0 

31-4 

33-8 

36.3 

38.8 

41-3 

43-7 

46.2 

48.6 

26 

7-5 

9-9 

12-5 

14.9 

17.5 

20.  O 

22.5 

25.0 

27.6 

30.1 

32-7 

35-2 

37-8 

40.4 

42.9 

45-4 

48.0 

50-5 

*7 

7.8 

10.3 

'3-0 

15-5 

18.2 

20.8 

23-4 

26.0 

28.6 

31-3 

33-9 

36.5 

39-2 

41.9 

44-5 

47-' 

49.8 

52.4 

28 

8.1 

10.7 

13-4 

1  6.  i 

18.9 

21-5 

24.2 

26.9 

29.7 

32.4 

35-2 

37-8 

40.6 

43-4 

46.  i 

48.8 

51-6 

54-3 

*9 

8.4 

ii.  i 

13-9 

16.7 

19.5 

22.3 

25-1 

27.9 

30.7 

33-6 

36.4 

39-2 

42.1 

45-0 

47-8 

50.6 

53-4 

56.2 

3° 

8.7 

11.5 

14.4 

17.2 

20.2 

23.1 

26.0 

28.9 

31.8 

34-7 

37-6 

40.5 

43-5 

46.5 

49-4 

52.3 

55-2 

58.2 

40 

11.5 

15-3 

19.2 

22.9 

26.9 

30.7 

34-6 

38.4 

42.3 

46.  i 

.50.0 

53-9 

57-8 

61.7 

65.6 

69.4 

73-3 

77-3 

5° 

14-4 

19.1 

23-9 

28.7 

33-5 

38.3 

43-2 

47-9 

52-7 

57-6 

62.4 

67.2 

72.1 

77.0 

81.8 

86.6 

91.5 

96.3 

I°00 

17.2 

22.9 

28.7 

34-4 

40.2 

46.0 

51-7 

57-5 

63.3 

69.0 

74.8 

80.6 

86.4 

92-3 

98.0 

104 

no 

"5 

I      10 

20.1 

26.7 

33-5 

40.1 

46.9 

53-6 

60.3 

67.0 

73-8 

80.5 

87-2 

93-9 

100.7 

107.5 

"4-3 

121 

128 

134 

I     20 

23-0 

30.5 

38.3 

45-8 

53-6 

61.2 

69.0 

76.6 

84.2 

91.9 

99-6 

107.3 

115-1 

123 

131 

138 

146 

154 

i    30 

25.8 

34-4 

43-0 

51.6 

60.3 

69.0 

77-7 

86.1 

94-7 

103.4 

112.  0 

120.7 

130 

138 

M7 

155 

164 

173 

i    40 

28.7 

38.a 

47-8 

57-3 

66.9 

76.6 

86.3 

95-6 

105.2 

"5 

124 

134 

144 

153 

163 

173 

182 

192 

i    50 

31.6 

42.0 

53.6 

63.0 

73-6 

84.2 

94-9 

105.2 

"5-7 

126 

137 

M7 

158 

169 

179 

190 

200 

211 

2     00 

34-4 

45-8 

57-4 

68.9 

80 

92 

103 

"5 

126 

138 

I49 

161 

172 

184 

195 

207 

218 

230 

2     30 

43-0 

57-3 

71.7 

86.0 

too 

"5 

129 

144 

158 

172 

186 

201 

215 

230 

244 

259 

273 

287 

3    00 

51.6 

68.8 

86.2 

103.2 

120 

138 

'55 

172 

190 

207 

224 

241 

259 

276 

293 

310 

328 

345 

3    3° 

60.2 

80.4 

100.5 

120.5 

141 

161 

181 

201 

221 

241 

261 

28l 

302 

322 

342 

362 

382 

402 

4   oo 

68.9 

91.8 

114.8 

137-7 

161 

184 

207 

230 

253 

276 

299 

322 

345 

368 

391 

414 

437 

460 

*  Curvature  and  refraction  taken  into  account  for  angles  of  elevation.    This  table  should  not  be  used  for  angles  of 
depression. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL.  33  5 

Example  of  use  of  table  of  heights. 

[Angle  of  elevation  from  point  A  to  point  B,  distant  from  each  other  1756  meters=i°  56'.] 

Meters.  Feet. 

i°  50' 1700 179.00 

i°  So' 50  5.26 

i°  5^ 6 63 

o°  06' 1700  10.  40 

o°  of/ 50 29 

o°  06' 6 04 


195-62 

Point  B  is  195.62  feet  above  point  A. 

Formula  for  determining  heights  by  a  vertical  angle  and  distance. — The  difference  of 
level  consists  of  two  parts — that  which  arises  from  the  angle  of  elevation  above  the 
horizontal  plane  of  the  station  and  that  which  is  due  to  the  curvature  of  the  earth. 
The  former  depends  upon  the  angle  and  distance,  the  latter  upon  the  distance  and  the 
earth's  radius.  If  a'  be  the  angle  of  elevation  in  minutes  of  arc,  d  the  distance,  h  the 
height,  then,  as  the  tangent  of  i'  is  -5^3-7,  we  have  for  the  first  part  h^^-fa^a'd,  if  h 
and  d  are  both  expressed  in  the  same  units  of  length,  but  if  d  is  expressed  in  meters 
and  h  in  feet,  one  meter  being  3.28  feet,  we  get  h—^-^a'd.  For  the  fraction  yaVg-  we 
may  conveniently  and  with  sufficient  accuracy  put  TTrVTr  less  -fa  of  TTnnr.  and  thus  find 
the  rule:  Multiply  the  distance  in  meters  by  the  number  of  minutes  of  arc,  point  off  the 
thousandth  part,  and  subtract  the  twentieth  part  of  the  number  thus  obtained.  This  will 
give  the  first  portion  of  difference  of  height,  whether  elevation  or  depression. 

The  second  term,  depending  on  the  curvature,  varies  as  the  square  of  the  distance, 
and  amounts  to  0.22  foot  in  1000  meters,  including  the  effect  of  ordinary  refraction. 
As  with  the  instruments  under  consideration  extreme  accuracy  is  not  attainable,  it  is 
plain  that  for  distances  under  1000  meters  this  term  may  be  neglected.  When  the 
distance  is  greater,  we  have  the  following  rule:  Take  the  thousandth  part  of  the  distance 
in  meters,  square  the  same,  having  regard  to  the  first  decimal  figure,  and  multiply  by 
0.22.  This  term  is  always  positive.  If  the  first  term  be  an  elevation,  it  is  increased;  if 
a  depression,  it  it  diminished  by  the  second  term. 

Example. — Distance =5500  meters;  angle  of  elevation,  36'. 

T5iiTjdXa'= 198.000  Tinnr^         =  5-5 

subtract  -£§       9.9  square       =30.2 

multiply  by  0.22 
first  term      188.1 
second  term     6.6  second  term   6.64 

sum  i94.7=difference  of  elevation  in  feet. 

75930"— 1 


336 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 

TABLE  II. —  Table  showing  the  height,  in  meters,  corre- 

( Curvature  and  refraction 


IOO 

200 

300 

400 

500 

600 

700 

800 

900 

1000 

I  IOO 

1  200 

0°       I' 

0.03 

0.06 

O.O9 

0.13 

o.  16 

o.  20 

o.  24 

o.  28 

0.32 

0.36 

o.  40 

0-45 

2 

o.  06 

0.  12 

o.  18 

0.24 

0.31 

0.37 

0-44 

0.51 

0.58 

0.65 

o.  72 

0.79 

3 

0.09 

o.  18 

o.  27 

0.36 

0.45 

0.55 

0.64 

0.74 

0.84 

0.94 

I.  04 

i.  14 

4 

0.  12 

0.24 

0.36 

0.48 

o.  60 

o.  72 

0.85 

0.97 

I.  10 

1.23 

1.36 

1-39 

5 

0.15 

o.  29 

0.44 

0-59 

0-74 

o.  90 

1.05 

I.  21 

1.36 

1-52 

1.68 

1.84 

o°    6' 

o.  18 

0.35 

0-53 

o.  70 

0.89 

I.  07 

1.26 

1.44 

1.62 

1.81 

2.  OO 

2.  19 

7 

o.  20 

0.41 

o.  62 

0.82 

1.04 

1.24 

1.46 

1.67 

1.89 

2.  10 

2.32 

2-44 

8 

0.23 

0.47 

o.  70 

0-94 

1.18 

1.42 

1.66 

I.  90 

2.16 

2-39 

2.64 

2.89 

9 

o.  26 

0-53 

0.79 

i.  06 

1-33 

1.59 

1.87 

2.14 

2.41 

2.68 

2.  96 

3-24 

10 

o.  29 

0.58 

0.88 

1.  18 

1.47 

i.77 

2.  07 

2-37 

2.68 

2.98 

3.28 

3-59 

0°    II7 

0.32 

0.64 

0.97 

i.  29 

1.62 

1.94 

2.  27 

2.  60 

2-93 

3-27 

3.60 

3-74 

12 

0.35 

o.  70 

1.05 

1.41 

1.76 

2.  12 

2.48 

2.84 

3-20 

3.56 

3-92 

4.29 

13 

0.38 

o.  76 

1.14 

1-52 

1.91 

2.  29 

2.68 

3-07 

3-46 

3-85 

4.24 

4-63 

14 

0.41 

0.82 

1.23 

1.64 

2.05 

2.47 

2.88 

3-30 

3-72 

4.14 

4.56 

4.98 

15 

0.44 

0.88 

1.32 

1.76 

2.  20 

2.64 

3.08 

3-53 

3.98 

4-43 

4.88 

5-33 

0°    \V 

0.47 

0-93 

i.  40 

1.87 

2.34 

2.82 

3-29 

3-77 

4.24 

4.72 

5-  20 

5-68 

17 

0.50 

0.99 

r.  49 

1.99 

2.49 

2-99 

3-49 

3.90 

4-50 

5-01 

5.52 

6.03 

18 

0.52 

1.05 

1.58 

2.  10 

2.  64 

3-  17 

3-70 

4-23 

4-77 

5-3° 

5.84 

6.38 

T9 

0.55 

I.  ii 

1.66 

2.22 

2.78 

3-34 

3-90 

4.46 

5-03 

5-59 

6.16 

6.63 

20 

0.58 

1.17 

1-75 

2-34 

2-93 

3.51 

4.11 

4-70 

5-29 

5-88 

6.48 

7.08 

0°    21' 

o.  61 

1.23 

1.84 

2-45 

3-07 

3-69 

4-31 

4-93 

5-55 

6.17 

6.80 

7-43 

22 

0.64 

1.28 

i-93 

2-57 

3-22 

3-86 

4.5i 

5-16 

5.8i 

6.47 

7.12 

7.78 

23 

0.67 

•34 

2.01 

2.69 

3.36 

4.04 

4-72 

5-40 

6.08 

6.76 

7.44 

8.12 

24 

o.  70 

.40 

2.  10 

2.80 

3-50 

4.21 

4-92 

5-63 

6-34 

7-05 

7.76 

8.47 

25 

0-73 

.46 

2.  19 

2.  92 

3-65 

4-39 

5-12 

5-88 

6.60 

7-34 

8.08 

8.82 

0°    26' 

o.  76 

•52 

2.28 

3-04 

3-80 

4.56 

5-33 

6.09 

6.86 

7-63 

8.40 

9.17 

27 

0.79 

•57 

2.36 

3-15 

3-95 

4-74 

5-53 

6-33 

7.12 

7.92 

8.72 

9-52 

28 

0.82 

.63 

2-45 

3-27 

4.09 

4.91 

5-74 

6.56 

7.38 

8.21 

9.04 

9-87 

29 

0.84 

.69 

2-54 

3-38 

4-24 

5-08 

5-94 

6.79 

7-65 

8.50 

9.36 

10.  22 

30 

0.87 

•  75 

2.  62 

3-5° 

4.38 

5-26 

6.  14 

7.02 

7.91 

8.79 

9.68 

10.57 

o°  40" 

i.  16 

2-33 

3-50 

4.66 

5-84 

7.00 

8.18 

9-35 

10.53 

II.  70 

12.88 

14.  06 

50 

1-45 

2.  91 

4-37 

5.83 

7.29 

8.75 

10.  22 

11.68 

I3.I4 

14.62 

16.08 

17-55 

oo 

1-75 

3-49 

5-24 

6.99 

8-74 

10.50 

12.  25 

14.01 

15.76 

17.52 

19.28 

21.  04 

10 

2.04 

4.08 

6.  12 

8.16 

10.  20 

12.  24 

14.29 

16.33 

18.38 

20.43 

22.48 

24.53 

20 

2-33 

4.66 

6.99 

9-32 

11.66 

13-99 

16.33 

18.66 

21.00 

23-34 

25.68 

28.03 

0  30' 

2.  62 

5-24 

7.86 

10.48 

13.11 

15-73 

18.36 

20.99 

23.62 

26.25 

28.88 

31.52 

40 

2.  91 

5-82 

8-74 

11.65 

14.56 

17.48 

2O.  40 

23.32 

26.  24 

29.  16 

32.09 

35-Qi 

5° 

3.20 

6.40 

9.  61 

12.82 

1  6.  02 

19.23 

22.44 

25-65 

28.86 

32.08 

35.29 

38.51 

2      OO 

3-49 

6.99 

10.48 

13-98 

17.49 

20.98 

24.48 

27.98 

31.48 

34-99 

38.49 

42.  oo 

2°   3C/ 

4-37 

8.74 

I3-H 

17.28 

21.85 

26.  22 

30.60 

34-97 

39-35 

43-73 

48.  ii 

52.49 

3    oo 

5-24 

10.48 

15-73 

20.97 

26.  22 

31.47 

36.72 

41-97 

47-22 

52-47 

57-73 

62.99 

3    30 

6.12 

12.  24 

18.36 

24.48 

30.  60 

36.72 

42.85 

44-97 

55-  10 

61.23 

67-36 

73.49 

4    oo 

6.99 

13-99 

20.98 

27-98 

34.98 

41.98 

48.98 

55.98 

62.99 

69.99 

77.00 

84.01 

IOO 

200 

300 

400 

5°o 

600 

700 

800 

900 

IOOO 

I  IOO 

I2OO 

*  Curvature  and  refraction  taken  into  account  for  angles  of 


APPENDIX  7.     A  PLANE  TABLE  MANUAL. 
spending  to  given  angles  of  elevation  and  distances  in  meters* 
taken  into  account. ) 


337 


1300 

1400 

1500 

1600 

1700 

1800 

1900 

2OOO 

2IOO 

22OO 

23OO 

2400 

2500 

0.49 

0-54 

0-59 

0.64 

o.  69 

0-74 

0.80 

0.85 

0.90 

0.96 

I.  02 

i.  08 

1.14 

0°       I' 

0.87 

0-95 

1.02 

I.  10 

1.18 

1.26 

1-35 

1-43 

1-52 

I.  60 

I.  69 

1.78 

1.87 

2 

1.25 

i-35 

I.46 

i-57 

1.68 

1-79 

i.  90 

2.01 

2.13 

2.  24 

2.36 

2.48 

2.60 

3 

1.63 

1.76 

1.90 

2.03 

2.  17 

2.31 

2-45 

2-59 

2-74 

2.  88 

3-03 

3-i8 

3-33 

4 

2.OO 

2.17 

2-33 

2.50 

2.67 

2-83 

3-o° 

3-18 

3-35 

3.52 

3-70 

3-88 

4-05 

5 

2.38 

2-57 

2-77 

2.  96 

3-i6 

3-35 

3-56 

3.76 

3-96 

4.16 

4-37 

4-57 

4.78 

o°     6' 

2.  76 

2.98 

3-20 

3-43 

3-66 

3-88 

4.  ii 

4-34 

4-57 

4.80 

5-04 

5-27 

5.5i 

7 

3-14 

3-39 

3-64 

3-89 

4-  15 

4.50 

4.66 

4.92 

5-i8 

5.44 

5.70 

5-97 

6.  24 

8 

3-52 

3-8o 

4.08 

4.36 

4-64 

4-93 

5-22 

5-50 

5-79 

6.08 

6-37 

6.67 

6.96 

9 

3-9° 

4.  20 

4-51 

4.82 

5-14 

5-45 

5-77 

6.08 

6.40 

6.  72 

7.04 

7.36 

7.69 

10 

4.27 

4.  61 

4-95 

5-29 

5-63 

5-98 

6.32 

6.67 

7.  01 

7.36 

7.71 

8.06 

8.42 

0°    II' 

4-65 

5-02 

5-39 

5-76 

6.13 

6.50 

6.87 

7-25 

7.62 

8.00 

8.38 

8.76 

9.14 

12 

5-03 

5-42 

5-82 

6.  22 

6.62 

7.  02 

7-43 

7.83 

8.24 

8.64 

9-05 

9.46 

9.87 

13 

5-41 

5-83 

6.26 

6.69 

7.12 

7-55 

7.98 

8.41 

8.85 

9.28 

9.72 

10.  16 

10.  60 

14 

5.78 

6.  24 

6.  70 

7-  15 

7.  62 

8.07 

8.53 

8-99 

9.46 

9.92 

10.39 

10.86 

11.32 

15 

6.16 

6.65 

7-  13 

7.62 

8.  ii 

8-59 

9.08 

9-58 

10.07 

10.56 

ii.  06 

".55 

12.05 

o°  16' 

6-54 

7-05 

7-56 

8.08 

8.60 

9.  12 

9-64 

10.  1  6 

10.68 

II.  20 

n-73 

12.25 

12.78 

17 

6.  92 

7.46 

8.00 

8-55 

9.09 

9.64 

10.19 

10.74 

ii.  29 

11.84 

12.  40 

12.95 

I3.5I 

18 

7-3° 

7-87 

8.44 

9.01 

9-59 

10.  16 

10.74 

11.32 

ii.  90 

12.48 

13.06 

13-65 

14-23 

19 

7.68 

8.28 

8.88 

9.48 

10.  08 

10.  69 

11.30 

ii.  90 

12.51 

13.12 

13-73 

14.35 

14.96 

20 

8.05 

8.68 

9-3i 

9-94 

10.58 

II.  21 

11.85 

12.48 

13.  12 

13.76 

14.40 

15.04 

15-  69 

0°    21' 

8.43 

9.09 

9-75 

10.  41 

11.07 

11.74 

12.  40 

13.07 

13-73 

14.40 

15.07 

15-74 

1  6.  42 

22 

8.  81 

9-50 

10.  19 

10.88 

n-57 

12.  26 

12.95 

13-65 

14-34 

15.04 

15-74 

16.44 

17.14 

23 

9.19 

9-9° 

10.  62 

n-34 

12.  06 

12.78 

13.51 

14-23 

14.96 

15.68 

16.41 

17.14 

17.87 

24 

9-57 

10.31 

ii.  06 

ii.  81 

12.56 

13.31 

14.  06 

14.81 

15-57 

16.32 

17.08 

17.84 

18.  60 

25 

9-94 

10.72 

11.50 

12.  27 

I3-05 

13.83 

I4.6l 

15-39 

16.  18 

16.96 

17-75 

18.54 

19.32 

0°    26' 

10.32 

11.13 

n-93 

12.74 

13-55 

14-35 

I5.I6 

15-98 

16.79 

17.  60 

18.42 

19.23 

20.05 

27 

10.  70 

ir-  53 

12.37 

13.20 

14.04 

14.88 

I5-72 

16.56 

17.40 

18.24 

19.09 

19-93 

20.78 

28 

11.08 

11.94 

12.80 

13-67 

14-53 

15.40 

16.  27 

17.14 

18.01 

18.88 

19.76 

20.63 

21.51 

29 

ii.  46 

12.35 

13.24 

14-  13 

15.03 

I5-92 

)6.  82 

17.72 

18.62 

19.52 

20.  42 

21-33 

22.  23 

30 

15-24 

16.42 

17.60 

18.79 

19.97 

21.  16 

22.35 

23-54 

24.73 

25.82 

27,  12 

28.31 

29.50 

o°  40' 

19.  02 

20.49 

21.97 

23-44 

24.92 

26.  40 

27.88 

29.36 

30.84 

32.32 

33-81 

35-29 

36.78 

50 

22.81 

24-57 

26.33 

28.10 

29.87 

31.64 

33-41 

35-i8 

36.95 

38.72 

40.50 

42.28 

44.  06 

I       00 

26.59 

28.64 

30.70 

32.75 

34-81 

36.87 

38.94 

41.  oo 

43.06 

45.13 

47-19 

49.26 

51-33 

I       10 

30.37 

32.72 

35-o6 

37.41 

39-76 

42.  10 

44.46 

46.82 

49-17 

51.53 

53.89 

56-25 

58.61 

I     20 

34.16 

36.79 

39-43 

42.07 

44-71 

47-35 

49-99 

52.64 

55-28 

57.93 

60.58 

63.23 

65.88 

i°  30' 

37-94 

40.87 

43.80 

46.73 

49-66 

52-59 

55-52 

58.46 

61.  40 

64.34 

67.28 

7O.  22 

73-16 

i     40 

41.72 

44-94 

48.16 

51.38 

54.61 

57.83 

61.  06 

64.28 

67-51 

70.74 

73-97 

77-21 

80.44 

i     5o 

45-50 

49.02 

52.53 

56.04 

59.56 

63-07 

66.59 

70.  10 

73.63 

77.15 

80.67 

84.  20 

87.72 

2    qo 

56.87 

61.26 

65.64 

70.03 

74-42 

78.81 

83.20 

87.59 

91.98 

96.38 

100.  78 

105.  17 

109.  57 

2°    30' 

68.24 

73-51 

78.76 

84.02 

89.29 

94-55 

99.82 

105.  10 

110.35 

115.62 

120.  89 

126.  16 

131-  44 

3     oo 

79-63 

85.76 

91.89 

98.03 

104.  1  8 

110.31 

116.45 

122.  59 

128.  74 

134.  88 

141.03 

147-  1  8 

153-  33 

3    3° 

91.02 

98.03 

105.  04 

112.06 

117.07 

126.  09 

133-  10 

140.  12 

147.  14 

154-  18 

161.  19 

168.  21 

175-  24 

4    oo 

1300 

1400 

1500 

1600 

1700 

1800 

1900 

2OOO 

2IOO 

2200 

2300 

2400 

2500 

elevation.    This  table  should  not  be  used  for  angles  of  depression. 


338 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Illustration  34  is  a  diagram  showing  the  method  of  constructing  a  scale  for  taking 
off  the  heights  corresponding  to  a  given  angle  and  distance. 

Table  of  factors  for  computing  differences  in  elevation.* 

To  obtain  the  difference  in  elevation  in  feet  multiply  the  horizontal  distance  in  meters  by  the 
factor  in  this  table  corresponding  to  the  observed  angle  of  elevation  or  depression.  The  factors  are 
given  for  each  ten  minutes,  but  the  value  for  the  nearest  minute  may  be  interpolated,  using  the  column 
of  differences  for  one  minute.  The  result  is  still  to  be  corrected  where  necessary  for  the  effect  of 
curvature  and  refraction. 

TABLE  III. 


Angle 

or 

!</ 

»/ 

3</ 

40' 

5°' 

60' 

Differ- 
ence for 
i  minute 
(fourth 
decimal 
place) 

o 

0 

o.  oooo 

0.0095 

0.0191 

0.0286 

o.  0382 

o.  0477 

o.  0573 

9-5 

I 

0.0573 

0.0668 

o.  0764 

0.0859 

0.0955 

o.  1050 

o.  1146 

9.6 

2 

o.  1146 

o.  1241 

o.  1337 

o.  1432 

o.  1528 

o.  1624 

o.  1719 

9-6 

3 

o.  1719 

o.  1815 

o.  1911 

o.  2007 

0.  2102 

o.  2198 

o.  2294 

9-6 

4 

o.  2294 

0.2390 

o.  2486 

o.  2582 

o.  2678 

o.  2774 

o.  2870 

9-6 

5 

o.  2870 

o.  2967 

0.3063 

0.3159 

o.  3255 

o.  3352 

o.  3448 

9.6 

6 

0.3448 

o.  3545 

o.  3641 

0.3738 

o.  3835 

o.  3932 

o.  4028 

9-7 

7 

o.  4028 

0.4125 

o.  4222 

0.4319 

o.  4416 

0.4514 

o.  4611 

9-7 

8 

o.  461  1 

o.  4708 

0.4806 

0.4903 

o.  5001 

0.5098 

0.5196 

9-8 

9 

0.5196 

0.5294 

o.  5392 

0.5490 

o.  5588 

0.5687 

o.  5785 

9.8 

10 

o.  5785 

o.  5884 

0.5982 

o.  6081 

0.6179 

o.  6278 

o.  6377 

9-9 

ii 

o.  6377 

o.  6476 

o.  6576 

0.6675 

o.  6774 

o.  6874 

o.  6974 

9-9 

12 

o.  6974 

o.  7073 

0.7173 

o.  7273 

o.  7374 

o.  7474 

o.  7574 

10.  0 

13 

o.  7574 

o.  7675 

o.  7776 

o.  7877 

o.  7978 

o.  8079 

o.  8180 

10.  I 

U 

o.  8180 

o.  8282 

0.8383 

o.  8485 

o.  8587 

o.  8689 

o.  8791 

IO.  2 

15 

o.  8791 

0.8893 

0.8996 

o.  9099 

o.  9201 

o.  9304 

o.  9408 

10.3 

16 

0.9408 

0.9511 

0.9615 

o.  9718 

o.  9822 

o.  9926 

1.0031 

10.  4 

17 

1.0031 

.0135 

.0240 

1.0344 

1.0449 

1.0555 

i.  0660 

IO-5 

18 

i.  0660 

.0766 

.0872 

1.0978 

I.  1084 

1.  1190 

i.  1297 

10.  6 

19 

i.  1297 

.1404 

.1511 

i.  1618 

I.  1726 

I.  1833 

i.  1941 

10.  7 

20 

1.1941 

.2050 

.2158 

i.  2266 

1.  2375 

1.  2485 

i.  2594 

10.  9 

21 

1-2594 

.2704 

.2813 

i.  2924 

1.  3034 

1.3144 

i.  3255 

II.  0 

22 

i-  3255 

.3367 

.3478 

1.3590 

1.  3702 

1.3814 

i.  3926 

II.  2 

23 

1.3926 

•  4039 

.4152 

i.  4266 

i.  4379 

1.4493 

i.  4607 

11.4 

24 

1.4607 

.4722 

.4836 

•4952 

1.5067 

1.5183 

1-5299 

"•5 

25 

•5299 

.5415 

•  5532 

•  5649 

1.5766 

1.5884 

1.6002 

11.7 

26 

.6002 

.6120 

.6239 

•6358 

1.6477 

1.6597 

1.6717 

11.9 

27 

.6717 

.6837 

.6958 

.7079 

i.  7200 

1.  7322 

1.7444 

12.  I 

28 

•  7444 

.7567 

.7690 

.7814 

i.  7937 

1.  8061 

i.  8186 

12.4 

29 

.8186 

.8311 

.8436 

.8562 

1.8688 

1.8815 

i.  8942 

12.6 

30 

.8942 

.9069 

.9197 

•9326 

i.  9454 

1.9584 

i.  9713 

12.9 

31 

•9713 

.9843 

•9974 

2.  0105 

2.  0236 

2.  0368 

2.  0501 

I3-I 

32 

2.  0501 

2.0634 

2.  0767 

2.0901 

2.  1036 

2.  II7I 

2.  1306 

13-4 

33 

2.  1306 

2.1442 

2.  1578 

2.  1715 

2-  1853 

2.  1991 

2.2130 

13-7 

34 

2.  2130 

2.  2269 

2.  2408 

2.  2548 

2.  2689 

2.  2831 

2.  2973 

14.0 

35 

2.  2973 

2-3"5 

2.  3258 

2.  3402 

2.  3546 

2.3691 

2-  3837 

14.4 

36 

2.3837 

2-  3983 

2.  4130 

2.4277 

2.4425 

2.  4574 

2.4723 

14.8 

37 

2.  4723 

2.  4873 

2.  5023 

2-  5175 

2-  5327 

2.  5479 

2.  5633 

15-2 

38 

2.  5633 

2.  5787 

2-5942 

2.6097 

2.  6253 

2.  6410 

2.  6568 

15-6 

39 

2.6568 

2.  6726 

2.6885 

2.  7045 

2.7206 

2-  7367 

2.  7530 

16.0 

40 

2-  7530 

2.7692 

2.  7856 

2.  8021 

2.  8l86 

2-  8353 

2.  8520 

16.5 

4i 

2.  8520 

2.8688 

2.  8857 

2.9026 

2-  9197 

2.9368 

2-  9541 

17.  o 

42 

2.  9541 

2.9714 

2.9888 

3.0063 

3.  0239 

3-  0416 

3-  0594 

17.6 

43 

3-0594 

3-0773 

3.0953 

3."34 

3-  1316 

3-  1499 

3-  1683 

18.  i 

44 

3.1683 

3.1868 

3-  2054 

3-  2241 

3-  2429 

3.  2618 

3.2808 

18.8 

*  Computed  by  G.  R.  Putnam,  Assistant,  Coast  and  Geodetic  Survey. 


APPENDIX  7.     A  PLANE  TABLE  MANUAL. 


339 


Table  of  corrections  for  curvature  and  refraction* 

The  correction  in  feet  for  the  combined  effect  of  curvature  and  refraction  is  given  for  each  loo 
meters'  distance,  the  thousands  of  meters  being  given  in  the  column  to  the  left  and  the  hundreds  in 
the  upper  line.  The  correction  is  to  be  added  to  the  difference  of  elevation  for  angles  of  elevation 
and  subtracted  for  angles  of  depression,  or  it  is  always  to  be  added  to  the  uncorrected  elevation  of  the 
point  to  be  determined  from  point  of  observation. 

Example:  At  a  station  whose  elevation  is  1000  feet  (at  telescope),  angle  to  signal=3°  elevation, 
horizontal  distance=sooo  meters.  From  Table  III  factor  is  0.1719,  which  multiplied  by  5000=859.5 
feet.  From  Table  IV  correction  is  5.5  feet.  Corrected  difference  of  elevation=859.5-4-5. 5=865  feet, 
which  added  to  1000=1865  feet  for  elevation  of  signal.  If  the  above  angle  to  signal  be  3°  depres- 
sion, then  corrected  difference  of  elevation =859. 5— 5.5=854  feet,  which  makes  height  of  signal= 
1000—854=146  feet. 

TABI,E  IV. 


Distance  in 
meters 

0 

IOO 

200 

300 

400 

500 

600 

700 

800 

900 

IOOO 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

o 

0.0 

o.  o 

o.  o 

o.  o 

0.0 

0.  I 

0.  I 

0.  I 

O.  I 

0.  2 

0.  2 

1000 

0.  2 

0-3 

o-3 

0.4 

0.4 

o.5 

0.6 

0.6 

0.7 

0.8 

0.9 

2000 

0.9 

I.O 

i.  i 

I.  2 

1-3 

1-4 

1-5 

1.6 

1-7 

i-9 

2.  O 

3000 

2.0 

2.  I 

2.3 

2.4 

2.6 

2.7 

2.9 

3-0 

3-2 

3.4 

3-5 

4000 

3-5 

3-7 

3-9 

4.1 

4.3 

4-5 

4-7 

4-9 

5-  i 

5-3 

5-5 

5000 

5-5 

5-8 

6.0 

6.2 

6.5 

6.7 

7.0 

7-2 

7-4 

7-7 

8.0 

6000 

8.0 

8.2 

8.5 

8.8 

9-i 

9-4 

9-7 

IO.  O 

10.  2 

10.6 

10.  9 

7000 

10.9 

II.  2 

ii.  5 

11.  8 

12.  I 

12.5 

12.8 

13.1 

13-5 

13.8 

14.2 

8000 

14.2 

14-5 

14.9 

15-3 

15-6 

16.  o 

16.4 

16.8 

17.2 

17.6 

18.0 

9000 

18.0 

18.4 

18.  8 

19.2 

19.  6 

20.  o 

20.4 

20.8 

21.3 

21.  7 

22.  2 

•       IOOOO 

22.  2 

22.6 

23.0 

23-5 

24.  o 

24.4 

24.9 

25.4 

25.8 

26.3 

26.8 

IIOOO 

26.8 

27-3 

27.8 

28.3 

28.8 

29-3 

29.8 

30-3 

30.8 

31.4 

31-9 

I2OOO 

31-9 

32.4 

33-  ° 

33-5 

34-1 

34-6 

35.2 

35-7 

36.3 

36.9 

37-4 

13000 

37-4 

38.0 

38-6 

39-2 

39-8 

40.4 

41.  o 

41.6 

42.  2 

42.8 

43-4 

14000 

43-4 

44.1 

44-7 

45-3 

46.0 

46.6 

47.2 

47-9 

48.5 

49.2 

49-8 

15000 

49-8 

50.5 

51-2 

51-9 

52.5 

53-2 

53-9 

54-6 

55-3 

56.0 

56.7 

16000 

56.7 

57-4 

58.2 

58.9 

59-6 

60.3 

61.  o 

61.8 

62.5 

63.3 

64.0 

17000 

64.0 

64.8 

65.6 

66.3 

67.1 

67.9 

68.6 

69.4 

70.2 

71.0 

71.8 

18000 

71.8 

72.6 

73-4 

74.2 

75-0 

75-8 

76.7 

77-5 

78.3 

79.1 

80.0 

19000 

80.0 

80.8 

81.7 

82.5 

83-4 

84.2 

85.1 

86.0 

86.9 

87.7 

88.6 

*  Computed  by  G.  R.  Putnam,  Assistant,  Coast  and  Geodetic  Survey. 


340 


COAST  AND  GEODETIC  SURVEY  REPORT,  1905. 


Table  of  factors  for  computing  differences  in  elevation. 

To  obtain  the  difference  in  elevation  in  meters,  multiply  the  horizontal  distance  in  meters  by  the 
factor  in  this  table  corresponding  to  the  observed  angle  of  elevation  or  depression.  The  factors  are 
given  for  each  ten  minutes,  but  the  value  of  the  nearest  minute  may  be  interpolated,  using  the  column 
of  differences  for  one  minute.  The  result  is  still  to  be  corrected  where  necessary  for  the  effect  of 
curvature  and  refraction. 

TABX.E  V. 


Angle 

tf 

iof 

20f 

vf 

4<y 

& 

6c/ 

Difference 
for  i  min- 
ute (4th  dec. 
place) 

o 

0 

o.  oooo 

o.  0029 

o.  0058 

0.0087 

o.  0116 

o.  0145 

0.0175 

2-9 

I 

.0175 

.0204 

•0233 

.0262 

.0291 

.0320 

•0349 

2.9 

2 

.0349 

.0378 

.0407 

•0437 

.  0466 

•  0495 

.0524 

2.9 

3 

.0524 

•0553 

.0582 

.  0612 

.  0641 

.  0670 

.0699 

2.9 

4 

.0699 

.0729 

.0758 

•  0787 

.0816 

.0846 

.0875 

2.9 

5 

.0875 

.0904 

•0934 

.0963 

.  0992 

.  1022 

•  1051 

2.9 

6 

.  1051 

.1080 

.1110 

•1139 

.  1169 

.  1198 

.  1228 

2.9 

7 

.  1228 

•  1257 

.1287 

.1317 

.1346 

•1376 

.1405 

2.9 

8 

.1405 

•1435 

.1465 

•1495 

•1524 

•1554 

.1584 

3-° 

9 

.1584 

.  1614 

.  1644 

•1673 

.1703 

•1733 

.1763 

3-o 

10 

.1763 

•1793 

.1823 

•1853 

.1883 

.1914 

.  1944 

3-o 

ii 

.1944 

•1974 

.  2004 

•2035 

.2065 

.2095 

.  2126 

3-0 

12 

.  2126 

.2156 

.2186 

.2217 

•  2247 

.2278 

.2309 

3-o 

13 

.2309 

•2339 

.2370 

.  2401 

.2432 

.  2462 

•2493 

3-i 

14 

•  2493 

•2524 

.2555 

.2586 

.  2617 

.2648 

.2679 

3-i 

15 

.2679 

.2711 

.2742 

•2773 

.2805 

•2836 

.2867 

3-i 

16 

.2867 

.2899 

.2931 

.  2962 

.2994 

.3026 

•3°57 

3-2 

17 

.3057 

.3089 

.  3121 

•3153 

•  3185 

•3217 

•3249 

3-2 

18 

•  3249 

.3281 

.3314 

•3346 

•3378 

•34H 

•3443 

3-2 

19 

•3443 

•3476 

.3508 

•3541 

•3574 

.3607 

•  3640 

3-3 

20 

.3640 

•3673 

.3706 

•3739 

•  3772 

.3805 

•3839 

3-3 

21 

•3839 

.3872 

.3906 

•3939 

•3973 

.4006 

.  4040 

3-3 

22 

.4040 

.4074 

.4108 

.4142 

.4176 

.  4210 

•4245 

3-4 

23 

•  4245 

•4279 

.4314 

•  4348 

•4383 

•4417 

•4452 

3-4 

24 

•  4452 

•4487 

.4522 

•4557 

•  4592 

.4628 

.4663 

3-5 

25 

.4663 

.4699 

•  4734 

.4770 

.4806 

.4841 

.4877 

3-5 

26 

.4877 

•4913 

•  4950 

.4986 

.5022 

•5059 

•5095 

3-6 

27 

.5095 

.5132 

•5169 

.5206 

•  5243 

.5280 

•5317 

3-7 

28 

.5317 

•  5354 

•5392 

•5430 

•  5467 

•5505 

•5543 

3-8 

29 

•5543 

.558r 

•  5619 

•5658 

.5696 

•5735 

•5774 

3-8 

30 

•5774 

.5812 

•5851 

.5890 

•5930 

.5969 

.  6009 

3-9 

31 

.6009 

.6048 

.6088 

.6128 

.6168 

.6208 

.6249 

4.0 

32 

.6249 

.6289 

•6330 

•6371 

.6412 

•6453 

.6494 

4.1 

33 

.6494 

•6536 

•6577 

.6619 

.6661 

•  6703 

•6745 

4-2 

34 

.6745 

.6787 

.6830 

.6873 

.6916 

•6959 

.  7002 

4-3 

35 

.  7002 

.7046 

.7089 

•7133 

.7177 

.  7221 

•7265 

4.4 

36 

•  7265 

.7310 

•  7355 

.7400 

•  7445 

.7490 

•7536 

4-5 

37 

.7536 

.758i 

.7627 

•  7673 

.  7720 

.7766 

•7813 

4.6 

38 

•7813 

.7860 

.7907 

•7954 

.  8002 

.8050 

.8098 

4-7 

39 

.8098 

.8146 

•8195 

.  8243 

.8292 

.8342 

•8391 

4-9 

40 

•8391 

.8441 

.8491 

•  8541 

.8591 

.8642 

.8693 

5-0 

4i 

.8693 

.8744 

.8796 

.8847 

.8899 

•8952 

.9004 

5-2 

42 

.9004 

•9°57 

.9110 

•9163 

.9217 

.9271 

•9325 

5-4 

43 

•9325 

.9380 

•9435 

.9490 

•9545 

.  9601 

•9657 

5-6 

44 

•9657 

•9713 

.9770 

.9827 

.9884 

•9942 

I.  OOOO 

5-7 

APPENDIX  7.     A  PLANE  TABLE  MANUAL. 


341 


Table  of  corrections  for  ciirvatiire  and  refraction. 

The  correction  in  meters  for  the  combined  effect  of  curvature  and  refraction  is  given  for  each  100 
meters  distance,  the  thousands  of  meters  being  given  in  the  column  to  the  left  and  the  hundreds  in 
the  upper  line.  The  correction  is  to  be  added  to  the  difference  of  elevation  for  angles  of  elevation 
and  subtracted  for  angles  of  depression,  or  it  is  always  to  be  added  to  the  uncorrected  elevation  of 
the  point  to  be  determined  from  point  of  observation. 

Example:  At  a  station  whose  elevation  is  304.80  meters  (at  telescope),  angle  to  signal  3°  eleva- 
tion, horizontal  distance  5000  meters.  From  Table  V  factor  is  0.0524,  which  multiplied  by  5  000= 
262.00.  From  Table  VI  correction  is  1.67  meters.  Corrected  difference  of  elevation =262. 00+ 
1.67=263.67  meters,  which  added  to  304.80=568.47  meters  for  elevation  of  signal.  If  the  above 
angle  to  signal  be  3°  depression,  then  corrected  difference  of  elevation  262.00—1.67=260.33  meters, 
which  makes  height  of  signal=3o4.8o — 260.33=44.47  meters. 

VI. 


Distance  in 
meters 

O 

IOO 

200 

300 

400 

500 

600 

700 

800 

900 

IOOO 

O 

O.  OO 

O.  OO 

O.  OO 

O.  OI 

O.  OI 

o.  02 

o.  02 

0.03 

0.04 

0.05 

o.  07 

IOOO 

0.07 

0.08 

0.  10 

0.  II 

o.  13 

o.  15 

0.17 

o.  19 

0.  22 

o.  24 

o.  27 

2OOO 

o.  27 

o.  29 

0.32 

o-35 

0.38 

o.  42 

0-45 

0.49 

0.52 

0.56 

o.  60 

3000 

o.  60 

0.64 

0.68 

0-73 

0.77 

0.82 

0.86 

0.91 

o.  96 

I.  01 

1.07 

4000 

1.07 

I.  12 

i.  18 

1.23 

i.  29 

1.35 

1.41 

1.47 

1-54 

1.  60 

1.67 

5000 

I.  67 

1.74 

i.  80 

1.87 

1.94 

2.  O2 

2.09 

2.  17 

2.  24 

2.32 

2.  40 

6000 

2.40 

2.48 

2.56 

2.65 

2.73 

2.82 

2.  91 

3.00 

3-09 

3.18 

3.27 

7000 

3.27 

3-36 

3-46 

3-55 

3-65 

3-75 

3-85 

3-96 

4.06 

4.  16 

4-27 

8000 

4.27 

4.38 

4-49 

4.  60 

4.7i 

4.82 

4-93 

5.05 

5-  16 

5-28 

5-40 

9000 

5-40 

5-52 

5.65 

5-77 

5-89 

6.02 

6.15 

6.28 

6.  41 

6.54 

6.67 

10000 

6.67 

6.80 

6.94 

7.08 

7-  22 

7-36 

7.50 

7.64 

7.78 

7-93 

8.07 

I  IOOO 

8.07 

8.22 

8-37 

8.52 

8.67 

8.82 

8.98 

9-13 

9.29 

9-45 

9.6l 

I2OOO 

9.61 

9-77 

9-93 

10.  09 

10.  26 

10.42 

10-59 

10.76 

10.  92 

II.  10 

II.  27 

13000 

II.  27 

H.45 

11.62 

11.80 

11.98 

12.  l6 

12.34 

12.52 

12.  71 

12.89 

13.08 

14000 

13.08 

13.26 

13-45 

13.64 

13.83 

14.03 

14.  22 

14.42 

I4.6l 

14.81 

15-01 

15000 

15.01 

15.21 

i5-4r 

15.62 

I5-82 

16.03 

16.24 

16.44 

16.65 

16.87 

17.08 

16000 

17.08 

17.30 

I7-5I 

17-73 

17-95 

18.  17 

18.  39 

18.61 

18.83 

19-05 

19.28 

17000 

19.28 

I9-5I 

19-73 

19.96 

2O.  19 

20.43 

20.66 

20.  89 

21.  13 

21-37 

21.  6l 

18000 

21.  6l 

21.86 

22.  IO 

22.34 

22.58 

22.83 

23.08 

23-33 

23.58 

23-83 

24.08 

19000 

24.08 

24-34 

24.60 

24.85 

25.  II 

25-37 

25-63 

25.89 

26.  15 

26.  42 

26.68 

Comparison  of  feet  and  meters. 
[i  meter =3. 280869  feet.] 


Meters. 

Feet. 

Feet. 

Meters. 

I  

3.  2808 

I 

o  1048 

2  

6.  5617 

2  

O  6096 

V  . 

Q.  8425 

•J    . 

O  QI44 

4.  . 

\\.  12^ 

4 

I    2192 

c    . 

1  6.  4O42 

K 

I    ^240 

6  

IQ.  68  SO 

6  

I.  8288 

7  

22.  06^8 

7  . 

2    1^6 

8  

26.  2467 

8 

2   4^84 

Q.  . 

2Q.  S27"; 

2   7432 

NOTE. 

The  following  illustrations,  Nos.  17  to  28,  show  the  conventional  signs  adopted  by 
the  United  States  Geographic  Board. 
342 


NO.  17. 


WORKS    AND    STRUCTURES 


Canal  or  Ditch 

Aqueduct  or  Water  pipe. 

Aqueduct  Tunnel )==„,=====« 

Canal  Lock  (point  up  stream)' _ 1 

Metaled ===== 

Good. ====_, 

Poor  or  Private =,„„„=„„====„===„==, 

On  small-scale  maps __^_ 

Trail  or  Path 

'Railroad  of  any  kind_.  ,,,,,,,,,,,,,, 

(or  Single  Track) 

Double  Track .  .  i  .  i  i  .  .  i  i  i  i  i  i 

Juxtaposition  of _;_ ,1,,  ,,.,.,., r 

Railroads     { 

Electric 

1/77  Wagon  Road  or  Street  Steam      ,£/ectn'c 

Tunnel t..*..,,.,*-*-*-*- 

Railroad  Station  of  any  kind .  ,  ,  ,  ,  ,  .,, 

{Symbol  (modified  6e/ou/)i    TTTTTTTT 
Along  road .    ,    , — ,    ,    ,    , 
Along  road , _ 
(small-scale  maps) 
Along  trail r.^..-r~r~r~r-r--f- 

Electric  Power  Transmission  Line 

(Fence  of  any  kind 

(or  board  fence) 

c 

"A  Worm .. v^s^~v~-~-^^^ — •~^~^^v 

fiarfecf     .         Smooth^ 


NO.  18. 


WORKS    AND    STRUCTURES 
CONTINUED 


'General  Symbol 


Drawbridges  (on  large-scale         / 
charts  leave  channel  open)  { 


Bridges  ) 


Truss  (  W,  Wood;  S,  Steel) 
Foot 

Suspension 

Arch 
.Pontoon 


Ferries 


Fords 


General  Symbol 
(or  Wagon  and  Artillery) 


t  Infantry  and  Cavalry 
Cavalry 


Dam 


Buildings  in  general 


Ruins 

Church 

Hospital 

Schoolhouse 

Post  Office 

Telegraph  Office 

Waterworks 

Windmill 


Jl 


WORKS    AND    STRUCTURES 
CONTINUED 


City,  Town,  or  Village 


NO.  19. 


City,  Town,  or  Villagefgeneralized) 


City,  Town,  or  Village 
(small-scale  maps) 


Capital 


County  Seat 


Other  Towns 


Cemetery 


Ufi 


Mine  or  Quarry  of  any  kind  (or  open  cut) 

Prospect 

Shaft 

Mine  Tunnel 


[Showing  direction 


OH  Wells 


Oil  Tanks  (abbreviation  OT) 
Coke  Ovens 


NO.  20. 


DRAINAGE 


Streams  in  general 

Intermittent  Streams-. 


Lake  or  Pond  in  general 

(with  or  without  tint,  waterlining.  etc.) 


Salt  Pond  (broken  shoreline  if  intermittent}. 


Intermittent  Lake  or  Pond. 


Glaciers 


LETTERING 


Names  of  natural  land  features,  vertical  lettering 
NaMS  of  natural  water  features,  slanting  lettenng 


NO.  21. 


RELIEF 

( Shown  by  contours,  form  lines,  or  shading  as  desired) 


Hill  Shapes 


Form  lines,  hachures. 

stipple, 
or  other  shading 


Contour  System 


Depression  Contours,  if  otherwise 
ambiguous,  hachured  thus 


Rooky  ( or  use  contours ) 


Bluffs     j 


Other  than  rocky  (or  use  contours) 


Sand  Dunes 


Levee 


NO   22. 


LAND    CLASSIFICATION 


/Marsh  in  general  (or  Fresh  Marsh} 


Marsh 


Salt 


Wooded 


\Cypress  Swamp 


Woods  of  any  kind  (or  as  shown  below) 


Woods  Of  any  kind  (or  Broad- Leaved  Trees} 


Pine  (or  Narrow-Leaved  Trees) 


Palm 


Palmetto.... 


NO.  23. 


LAND    CLASSIFICATION 
CONTINUED 


Mangrove 


Bamboo 


Cactus 


Banana. 


Orchard 


Grassland  in  general 


Tall  Tropical  Grass... 


Cultivated  Fields  in  general.. 


<&  « 


NO.  24. 


Cotton. 


Rice..—. 


Sugar  Cane ... 


*  {  T.  t  1"f  f  T 

*  f  1  T  t  ?  f 

LiLiiJLL!  i- 

Corn.... 


BOUNDARIES, 
MARKS.  AND  MONUMENTS 

National,  State,  or  Province  Line 

County  L/ne__  ......................  .  ....................................... 


C/v/7  Township,  District, 
Precinct,  or  Barrio 

Reservation  Line 


Land-Grant  Line  ...........  . 

City,  Village,  or  Borough 
Cemetery,  Small  Park,  etc 


Township,  Section,  and  Quarter  Section 

Lines  (any  one  for  township  line  alone,  any 
two  for  township  and  section  lines) 


Township  and  Section  Corners  Recovered— + .j. +.... 

Boundary  Monument 
Triangulation  Station 

Bench  mark 

U.  S.  Mineral  Monument 


BXM 

1232 


NO.  25. 


HYDROGRAPHY,  DANGERS,  OBSTRUCTIONS 


Shorelines 


Surveyed 

Unsurveyed 


Shores 
Low-  Water  Lines 


'Tidal  Flats  of  any  kind 
(or  as  shown  below) 


Rock  awash  (at  any  stage  of  the  tide) *   & 

Rock  whose  position  is  doubtful ..._ *  PT> 

Pock  whose  existence  is  doubtfuL. „ S  ZD 


NO.  26. 

HYDROGRAPHY,  DANGERS,  OBSTRUCTIONS 
CONTINUED 


Overfalls  and  Tide  Rips 

Limiting  Danger  Line 

Whirlpools  and  Eddies 

Wreck  Of  any  kind  (or  Submerged  Derelict) 

Wreck  or  Derelict  not  submerged 

CaWe  (with  or  without  lettering) 

Current,  not  tidal,  velocity  2  knots 

f  Flood,  1'Aknots J*.  *» 

Ebb,  1  knot '** 

Tidal  Currents 

Flood,  2d  hour. 


\Ebb.3dhour ^^,    or-    HH-* 

No  bottom  at  50  Fathoms So     So 

Depth  Curves 

1  Fathom  or  6  Foot  Line 

2  Fathom  or  12  Foot  Line 

5  Fathom  or  18  Foot  Line. 

4  Fathom  Line 

4'A  Fathom  Line 

5  Fathom  Line 

6  Fathom  Line 

10  Fathom  Line 

20  Fathom  Line  , 

30  Fathom  Line 
40  Fathom  Line 
SO  Fathom  Line.  — — —  —  - 


NO.  27. 

HYDROGRAPHY.  DANGERS.  OBSTRUCTIONS 
CONTINUED 

700  Fathom  Line 

200  Fathom  Line. 

300  Fathom  Line 

500  Fathom  Line 

1000  Fathom  Line. _ _ _ 

2000  Fathom  Line 

3000  Fathom  Line 


Abbreviations  relating  to  Bottoms 

M.  mud,  S.  sand,  G.  gravel,  Sh.  shells,  P.  pebbles,  Sp.  specks, 
CI.  clay,  St.  stones,  Co.  coral,  Oz.  ooze,  bk.  black,  wh.  white,  rd  red, 
yl.  yellow,  gy.  gray,  bu.  blue,  dk.  dark,  11.  light,  gn.  green,  br.  brown, 
hrd.  hard,  sft.  soft,  fne.  fine,  crs.  coarse,  rky.  rocky,  stk.  sticky 
brk.  broken,  Irg.  large,  sml.  small,  stf.  stiff,  cat.  calcareous,  dec. 
decayed,  rot.  rotten,  spk.speckled,  fly.  flinty,  gty.  gritty,  grd.  ground, 
str.  streaky,  vol. volcanic. 


AIDS    TO    NAVIGATION.  ETC. 

Life-saving  Station  ^,  iss  (T) 

[(T)  indicates  telegraphic  connection] 
Light  of  any  kind  (or  Lighthouse). jj. 

Lighthouse,  on  small  scale  chart • 

Light  Vessel  of  any  kind ^ 

Light  Vessels  showing  number  of  masts -^  •&  sJi. 

Light  with  Wireless fi&    «, 

'fyy 

Light  Vessel  with  Wireless, _ (£) 

Light  with  Submarine  Bell. w    - 

Light  Vessel  with  Submarine  Bell —     4" 

Light  with  Submarine  Bell  and  Wireless __.(g)   ^ 

Light  Vessel  with  Submarine  Bell  and  Wireless (T) 


NO.  28. 

AIDS    TO    NAVIGATION.  ETC. 
CONTINUED 

(Lighted.  *    * 

Beacons  J 

\Not lighted-.-.  Bn*.  1  i  I  I  I  1 

Sectors,  shown  by  dotted  lines 

Abbreviations  relating  to  Lights 

F.  fixed,  Fig.  flashing,  PI.  flash,  Fls.  flashes,  Sec.  sector,  Rev.  revolv- 
ing, E.  electric,  W.  white,  R.  red,  V.  varied  by,  Grp.  group,  Occ, 
occulting,  Int.  intermittent.  Alt  alternating,  m.  /n;/es,  min.  m/nutes, 
sec.  seconds. 

/  0 

Buoy  of  any  kind  (or  Red  Buoy)  -     • 

B/ac* 

Striped  horizontally 

4> 
Striped  vertically 

• 

Checkered -••••          • 

Buoys  < 

Perch  and  Square 

Perc/J  and  Ball 

5  J5  $ 

Whistling  (oruse  first  four  symbols  :  T  :  I 

wrt/i  word  "  whistling  ")  414. 

SeW  ( or  use  first  four  symbols  with  jit! 

word  "bell")  ^ 

\Lighted *• 

Spindle  or  Stake  (add  word  " spindle':  I 

if  space  allows) 

Abbreviations  relating  to  Buoys 

C   can,  N.  nun,  S.  spar,  H.  S.  horizontal  stripes,  B.  black,  R.  red, 
W.  white,  V.  S.  vertical  stripes,  C.  green,  Y.  yellow,  Ch.  checkered. 

I  Of  any  kind  ( or  for  large  vessels )  i 

Anchorage   J 

\  For  small  vessels t- 

Mooring  Buoy  * 

Range  or  Track  Line   _ 


1 

S.JA//O 

rfcirc 

'ANNELS 

O 

rWXYZ 

rWXYZ 

t^1 

> 

0. 

^ 

o 

0 

% 
• 

r^ 

H^ 
C 

ENGRA\ 

DIVISIOl 

CAPITOL 

HARBOR 

ISLANDS 

RIVERS 

SOUNDINGS 

DIRECTIONS 

*oints  POINTS 

in 

u 
u 

K 
O 

u 

(0 

111 

Z 

z 
«< 

X 

o 

SIVOHS  sjntn 

^*t_^^ 

CT5 

Q 

PH 

>PQRSTL 

ing 

«*( 

° 

0 

CO 

O 

*o  s 

O 

1 

1 

OP 

0) 

13 

0 

CO 

-a 

^^^^i 
^^^^^ 

r^     ^ 

L                     * 

^   "g 

1—  1 

£ 

5 

Jq 

U 

o 

£ 

^^M 
^^^^1 

k^    | 

> 

Z 

^N^^^fl 

^'^^J 

^ 

NGRA 

O 

HH 
HH 
HH 

APITOL 

ffj 
O 
ffl 

i  LANDS 

VERS 

)UNDINGS 

RECTIONS 

[NTS  P  OINTS 

IEKS  CREEKS 

VNELS  CHANNELS 

LB  SHOALS 

FGHIJ 

1 

H 

Q 

O 

as 

VJ 

t—  i 

^-i 

w 

CO 

M 

Q 

^H 

o 

m 
u 

3 

V 

m 

H 

fcq 

T  M 

Q 

Q 

§K        O 

in 

0 

in 

o 

in 

o 

tO 

o 

in 

f\4 

^^^ 

^^^ 

H      <fl 

in 

in 

CO 

ga 

O 

o 

PQ 

^ 

No.  80 


Sparsely  settled  Town.  Salt  Marsh,  Pine  Woods,  Ditches,  Fence*,  and  Undefined  Roads 


No.  81 


Railroads,  Canals,  Iron  Bridges,  Rocky-cliffs,  Mid-river  drift,  Water-worn  Rocks,  Mixed  Woods  over  hill  curves  (Harpers  Ferry) 


No.  82 


\  ijn  (  ;  s1// ^-      xw.  xr^i  — Hf?a 

>H<fe4o/^i^"'^ii 


Eroded  drift  banks,  with  boulders  set  free  ;  and  scrub  deciduous  woods  (Gay  Head) 


No.  88 


•*\-e 


.^-Tis:;?'i<  kiag^a  ofti=-  s^s  k. 

-4" 

^^  •  f •  SB 

Ta^^fS^u^7^«^s^  ^ss?flyLaE>Vi 


r««iwcBiwrs'rj  *  _\s.  •  4  C-1  V  " L_--= 


Mocking  of  Cities.  Large  Buildings,  Suburban  Villas  and  Grounds,  Fresh  Marsh 


No.  34 


Erosion  of  Soft  fttrntififd  Rock  and  Gulch  (Santa  Cruz,  California) 


NO.  35. 


Hill  Curves  for  every  20  feet  difference  of  level.   Scale  TO; 


*Q 

V 

»n 

°O 

Slope 

Proportion 
of 

Length  of  Base 

Length  of  Base 

Length  of  Base 

°0 
0 

CO 

tf 

"o 

<N 

v 

*O 

tf5 

*•* 

*» 

r 

2° 
3° 
4° 
5° 
10° 
15° 
20° 
25° 
30° 
35° 
40° 
45° 
50° 
55° 
60° 

Height  to  Base 
1  to  57 
1   to  29 
1  to  19 
1  to  14 
1   to  11 
1  to  6 
1  to  4 
1  to  3 
1  to  2 
1  to  1.7 
1  to  1.4 
1  to  1.2 
1  to  1 
1  to  0.8 
1  to  0.7 
1  to  0.6 

(  in  feet.) 
57.  29 
28  .64 
19  .08 
14.  30 
11.43 
5.67 
3  .  73 
2  .75 
2  .  14 
1  .73 
1  .43 
1  .  19 
1  .00 
O.84 
0.70 
0.  58 

(  in  feet.) 
1145  .  8 
572.8 
381.6 
286.0 
228.6 
113.4 
74.6 
55.0 
42.8 
34.6 
28.6 
23.8 
20.0 
16.8 
14.0 
1L.6 

(  in  meters.) 
349.1 
174.  5 
116  .  3 
87.1 
69.7 
34.6 
22.  7 
16.7 
13.1 
10.  5 
8.  7 
7.  2 
6.1 
5.1 
4.3 
3.6 

01 

«• 

IE 
(f) 

u_ 
O 

UJ 


CO 

LJ 

> 

cc 

ID 

CO 
O 


00 


<    o 


NO.  37. 


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